# Solving Quadratic Equations by Completing the Square Review...

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Revised 04/10 1 HFCC Math Lab Intermediate Algebra 19 SOLVING QUADRATIC EQUATIONS BY COMPLETING THE SQUARE The easiest way to solve quadratic equations is by factoring. Since not all quadratic equations will factor we need another method that can be used to solve any quadratic equation. This method is called completing the square. In order to solve quadratic equations by Completing the Square method, you need to know how to complete the square for a binomial of the form 2 . x bx Recall from factoring that the trinomial 2 8 16 x x is a perfect square trinomial since it can be written as 2 ( 4) . x Notice that 2 8 16 2 . That is, the square of one-half the coefficient of the middle term equals the constant term, 16. In general, if 2 x bx c is a perfect square trinomial, then c is equal to the square of one-half b , that is, 2 2 b c . Note that the numerical coefficient of the 2 x term must be 1 in the above discussion. In summary, to make a binomial 2 x bx a perfect square trinomial of the form 2 x bx c , you add 2 2 b c to it. Ex 1: Complete the square for 2 10 x x 10 b 2 10 25 2 c 2 2 b c 2 10 25 x x add 25 c to 2 10 x x ( 5)( 5) x x factor the perfect square trinomial 2 ( 5) x rewrite with an exponent
Revised 04/10 2 Ex 2: Complete the square for 2 5 x x 5 b 2