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Topic: Completing the square

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	PlanetMath: completing the square (Site not responding. Last check: 2007-10-18)
		Completing the square can also be used to find the extremal value of a quadratic polynomial [2] without calculus.
		Completing the square can also be used as an integration technique to integrate, say
		This is version 8 of completing the square, born on 2003-05-02, modified 2005-03-18.
	planetmath.org /encyclopedia/CompletingTheSquare.html (117 words)

	Completing the Square: Circle Equations
		The technique of completing the square is used to turn a quadratic into a squared binomial, plus some loose numbers:
		, completing the square can be necessary for finding the center and radius of a circle, once you've been given the equation.
		Whatever is multiplied on the squared terms (it'll always be the same number!), divide it off from every term.
	www.purplemath.com /modules/sqrcircle.htm (456 words)

	Completing the Square: Solving Quadratic Equations
		For your average everyday quadratic, you have to use the technique of completing the square to rearrange the quadratic into the neat format demonstrated above.
		But in most other cases, you should assume that the answer should be in "exact" form, complete with all the square roots.
		When you complete the square, make sure that you are careful with the sign on the x-term when you multiply by one-half.
	www.purplemath.com /modules/sqrquad.htm (502 words)

	Completing the Square (Site not responding. Last check: 2007-10-18)
		Completing a square means looking for a constant term that makes this a perfect square trinomial.
		To begin completing a square, we need to multiply (or divide) every term by a constant so the x² coefficient is a perfect square.
		Let a be the x² coefficient, which is a perfect square, and b be the x coefficient.
	mcraefamily.com /MathHelp/factoring3b.htm (649 words)

	Solving Equations Algebraically
		The method of completing the square will always work, even if the solutions are complex numbers, in which case we will take the square root of a negative number.
		The result of completing the square on this general equation is a formula for the solutions of the equation called the Quadratic Formula.
		We are saying that completing the square always works, and we have completed the square in the general case, where we have a,b, and c instead of numbers.
	www.uncwil.edu /courses/mat111hb/Izs/asolve/asolve.html (2129 words)

	Completing the square (Site not responding. Last check: 2007-10-18)
		In completing the square, you are trying to take a quadratic equation and convert it into a perfect square trinomial.
		Now, the method of completing the square requires us to take 1/2 of the first order coefficient, square it and add it to both sides of the relation.
		The goal of completing the square is to take a quadratic trinomial and through manipulation, convert it into a perfect square trinomial.
	home.earthlink.net /~ubingc/math/mth209/soln2.htm (692 words)

	Math Forum - Ask Dr. Math Archives: Completing the Square
		I have to solve two equations by completing the square...
		I thought completing the square only involved quadratic functions, such as f(x) = ax^2 + bx + c = 0.
		The Math Forum is a research and educational enterprise of the Drexel School of Education.
	www.mathforum.org /library/drmath/sets/select/dm_complete_square.html (235 words)

	Jiskha Homework Help - Mathematics: Algebra: Completing the Square
		When the highest exponent of an equation is 2, the method of "Completing the Square" gives us an alternative.
		The strategy used in completing the square is to get the square of a quantity equal to a number as in
		Determine the coefficient of the x term, divide it by two, square it, and add to both sides.
	www.jiskha.com /mathematics/algebra/completing_the_square.html (413 words)

	Completing the Square
		The square root property cannot be directly applied in a quadratic that has a middle term such as
		We have seen that the square root property only worked when the middle term was zero.
		Below is a step by step process of completing the square.
	www.ltcconline.net /greenl/courses/152b/QuadraticsLineIneq/compsq.htm (279 words)

	2. Completing the Square (Site not responding. Last check: 2007-10-18)
		For quadratic equations that cannot be solved by factorising, we use a method which can solve ALL quadratic equations called completing the square.
		(iii) Complete the square by adding the square of one-half of the coefficient of x to both sides.
		Step (iii) Complete the square by adding the square of one-half of the coefficient of x to both sides.
	www.intmath.com /QuadEqns/2_ComSq.php (163 words)

	Completing the square - Wikipedia, the free encyclopedia
		Completing the square is an algebra technique, also used in many types of calculus.
		The essential objective is to reduce all instances of the variable in an equation or expression to be the same order.
		Completing the square reduces any problem involving a quadratic polynomial to one involving a square quadratic polynomial and a constant.
	en.wikipedia.org /wiki/Completing_the_square (307 words)

	Algebra Help - Completing the Square
		The technique of completing the square is presented here primarily to justify the quadratic formula, which will be presented next.
		In analytic geometry, for example, completing the square is used to put the equations of conic sections into standard form.
		The technique of completing the square is to take a trinomial that is not a perfect square, and make it into one by inserting the correct constant term (which is the square of half the coefficient of x).
	www.helpalgebra.com /onlinebook/completingthesquare.htm (351 words)

	This method is used to solve quadratic equations when the quadratic will not factor (Site not responding. Last check: 2007-10-18)
		What we want to put in each of the two blanks is a constant that will turn the quadratic expression into a perfect square trinomial (hence we will be "completing the square").
		On the one side, write the quadratic as its square root squared, and on the other side, combine the constant terms.
		Note: The square root of a perfect square quadratic trinomial with leading coefficient 1 is (x + half the coefficient of the linear term).
	www.math.unt.edu /mathlab/this_method_is_used_to_solve_qua.htm (222 words)

	ComplSquare
		"Completing the square" requires a small amount of thought to carry through, while the quadratic formula provides a means for solving quadratics by just "turning the crank".
		This simple transformation allows us to use the special method for solving equations where the left side is a square and the right side is a number.
		This formula can be used instead of the algorithm for completing the square.
	www.ii.uib.no /~wagner/hsalg/ComplSquare.htm (445 words)

	Algebra II Recipe: Completing the Square (Site not responding. Last check: 2007-10-18)
		"a" is the square root of the first term.
		"b" is the square root of the last term.
		The operation in the binomial will be the same as the operation in front of the "x" term.
	www.algebralab.org /studyaids/studyaid.aspx?file=Algebra2_5-5.xml (120 words)

	Math Help - Algebra - Quadratic Equations - Complete the Square - Technical Tutoring
		One way to deal with quadratic equations is completing the square, where one takes an equation that does not quite resolve into a nice squared linear factor, such as
		Even though this equation can be solved by simpler means, we are looking at using the complete the square formula, so add 1 to both sides and put in a "ghost" or zero term to hold the "x" place:
		This is as expected, and verifies that complete the square agrees with common sense.
	www.hyper-ad.com /tutoring/math/algebra/Complete_square.html (610 words)

	Completing the square - A complete course in algebra
		Completing the square - A complete course in algebra
		IN LESSON 18, we saw a technique called completing the square.
		To prove the quadratic formula, we complete the square.
	www.themathpage.com /alg/complete-the-square.htm (328 words)

	Completing the square
		Completing the square requires relatively basic manipulation of quadratic equations.
		(which is the square of the 'a' coefficient in the x term above) within the brackets.
		Although these 3 steps to completing the square may seem complicated, let us try some examples to clarify our understanding.
	www.algebra-help.info /completing-the-square.php (281 words)

	Completing the square - Topics in precalculus
		Therefore, we use a technique called completing the square.
		This means to make the quadratic into a perfect square trinomial, i.e.
		The sum of those roots is −6, which is the negative of the coefficient of x.
	www.themathpage.com /aPreCalc/complete-the-square.htm (235 words)

	Untitled Document
		Students will be able to transform the completed square function to an expanded function and back.
		With the completing the square, we are better able to see how the graph is transformed.
		The general procedures that will be followed to complete the square will be taking half the b term and squaring it and then making sure the you add the correct term to keep the equation balanced.
	www.bsu.edu /web/kaspencer/completesquare.html (994 words)

	Completing the Square (Site not responding. Last check: 2007-10-18)
		that is needed to form the perfect square.
		Here are three more examples of completing the square.
		Notice that Example 5 illustrates that completing the square can be applied to the same equation more than once, depending on how many variables appear as squares.
	www.math.csusb.edu /math110/src/tools/comp_square.html (225 words)

	The Quadratic Formula Explained
		from the process of completing the square, and is formally stated as:
		And make sure that you are careful not to drop the square root or the "plus/minus" in the middle of your calculations, or I can guarantee that you will forget to "put them back" on your test, and you'll mess yourself up.
		is negative, because the square of a negative is a positive.
	www.purplemath.com /modules/quadform.htm (458 words)

	MathsDirect (Site not responding. Last check: 2007-10-18)
		This method of solving quadratic equations is called Completing the Square.
		We will look at this in a moment, but first let's look at a few examples of completing the square.
		From these examples you should be able to see that once the correct number to add has been found, the method is straight forward.
	www.mathsyear2000.org /alevel/pure/purtutalgqua1.htm (144 words)

	Solution by completing the square
		is always the square of the second term of the
		Essentially, in completing the square, certain quantities are added to one member and
		based on completing the square has been developed in which known quantities may be substituted in order to derive the roots of the quadratic equation.
	www.tpub.com /math1/17b.htm (231 words)

	Quadratic Polynomials: Completing the Square
		If guessing does not work, "completing the square" will do the job.
		Next we take square roots of both sides, but be careful: there are two possible cases:
		The rest is easy: we take square roots of both sides, but be careful: there are two possible cases:
	www.sosmath.com /algebra/factor/fac07/fac07.html (559 words)

	[No title] (Site not responding. Last check: 2007-10-18)
		One way to solve this particular equation is by completing the square.
		Then we proceed to add a number squared to both sides of the equation to complete the square as follow:
		Use completing the square when you cannot factor the equation.
	cs.gmu.edu /cne/modules/dau/algebra/equations/quad2_bdy.html (347 words)

	Illuminations: Proof Without Words: Completing the Square
		The side length of the yellow square is x, and the width of the blue rectangle is a.
		This new arrangement is almost, but not quite, a complete square.
		After the square has been completed, adjust the slider for the Rectangle Width (a).
	illuminations.nctm.org /ActivityDetail.aspx?ID=132 (352 words)

	Completing The Square
		Recall the relationship between the constant in the binomial and the coefficients that occur in a trinomial square.
		To use the technique of completing the square to solve a quadratic equation, the coefficient of the leading term must be 1.
		Using the addition property, move the constant term to the other side of the equation, isolating it from the variable terms.
	www.jcoffman.com /Algebra2/ch5_7.htm (249 words)

	Perfect Squares and Completing the Square (C)
		Perfect Squares and Completing the Square (C) A quadratic expression of the form Az
		Sometimes there is more that one variable, and we can complete the square variable by variable:
		In each case write as a sum or difference of squares.
	www.uwm.edu /~ericskey/TANOTES/Algebra/node9.html (250 words)

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