# Solving Quadratic Equations by Completing the Square

Factoring Polynomials by Completing the Square Perfect Square Trinomials Examples x2 + 6x + 9 x2 - 10x + 25 x2 + 12x + 36 Creating a Perfect Square Trinomial

In the following perfect square trinomial, the constant term is missing. X2 + 14x + ____ Find the constant term by squaring half the coefficient of the linear term. (14/2)2 X2 + 14x + 49 Perfect Square Trinomials Create perfect square

trinomials. x2 + 20x + ___ x2 - 4x + ___ x2 + 5x + ___ 100 4 25/4 Factoring Quadratics by Completing the Square Factor by completing the square: 2

Step 1: First take the coefficient of the linear term, divide it by 2, and then square it. This gives 16 - (8/2)2 x +8x- 20 2 x +8x- 20 Factoring by Completing the Square Step 2: Add and subtract 16 just

after the linear term. Therefore, you did not change the value of the expression. x +8x+16 - 16+20 2 Factoring by Completing the Square Step 3: Use brackets to group the first three terms This is your perfect square trinomial. (x +8x+16)- 16+20 2

Factoring by Completing the Square Step 3: Factor the perfect square trinomial and simplify the rest. (x +8x+16)- 16+20 2 (x + 4)2 + 4 X2 12x + 4

Step 1: First take the coefficient of the linear term, divide it by 2, and then square it. Step 2: Add and subtract 16 just after the linear term. Therefore, you did not change the value of the expression. Step 3: Use brackets to group the first three terms This is your perfect square trinomial. Factor by Completing the Square Step 1: First take the coefficient of the linear term, divide it by 2, and then square it. Step 2: Add and subtract 16 just after the linear term. Therefore, you did not change

the value of the expression. Step 3: Use brackets to group the first three terms This2is your perfect square trinomial. 7 x - x+6 2 Solving Quadratic Equations by Completing the Square Step 4: Take the square root of each side

7 2 - 47 (x - ) 4 16 7 - 47 ( x - ) 4 4 7 i 47 x 4 4 7 i 47

x 4 Solving Quadratic Equations by Completing the Square Try the following examples. Do your work on your paper and then check your answers. 2 1. - 9, 7 2 2.(6, - 14) 2

3. - 3,8 1. x + 2 x - 63 0 2. x + 8 x - 84 0 3. x - 5 x - 24 0 2 4. x + 7 x + 13 0 5. 3 x 2 +5 x + 6 0 - 7 i 3 4. 2

- 5 i 47 5. 6

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