Precalc0011to0016-page7

Precalc0011to0016-page7 - and isolating a constant term on...

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(Section 0.11: Solving Equations) 0.11.7 Completing the Square (“CTS”) Method This method creates a perfect square trinomial (PST) , which can be factored as the square of a binomial. That square is then isolated , and the Square Root Method is applied. • This method is especially convenient when a = 1 and b is even. • Other cases will be discussed in Section 2.2 and Chapter 10. • The Quadratic Formula is actually derived using this method. • CTS will be used in Sections 0.13 and 2.2 and Chapter 10 to set up standard forms for equations of conics. Example 5 (Using the “CTS” Method) Solve x 2 + 8 x + 5 = 0 using the “CTS” Method. § Solution We begin by isolating the x 2 and x terms on one side of the equation
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Unformatted text preview: and isolating a constant term on the other side. x 2 + 8 x + 5 = x 2 + 8 x = ± 5 The coefficient of x 2 is 1, so we may now complete the square . We accomplish this by adding 16 to both sides of the equation. Why 16? We obtain the number we must add by taking the coefficient of x (here, 8), halving it (resulting in 4), and then squaring the result (the square of 4 is 16). x 2 + 8 x + 16 = ± 5 + 16 WARNING 9 : Do not forget to add 16 to the right-hand side, also. We now have a PST on the left-hand side. x + 4 ( ) 2 = 11 by factoring the PST ( ) x + 4 = ± 11 by the Square Root Method ( ) x = ± 4 ± 11 Technically, the solution set is: ± 4 ± 11 , ± 4 + 11 { } . §...
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This document was uploaded on 12/29/2011.

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