EXAMPLE 1 Solve a quadratic equation by finding square roots

Solve x2 – 8x + 16 = 25.x2 – 8x + 16 = 25 Write original equation.

(x – 4)2 = 25 Write left side as a binomial squared.

x – 4 = +5 Take square roots of each side.

x = 4 + 5 Solve for x.

The solutions are 4 + 5 = 9 and 4 –5 = – 1.

ANSWER

EXAMPLE 2 Make a perfect square trinomial

Find the value of c that makes x2 + 16x + c a perfect square trinomial. Then write the expression as the square of a binomial.

SOLUTION

STEP 1Find half the coefficient of x.STEP 2

162 = 8

Square the result of Step 1. 82 = 64STEP 3Replace c with the result of Step 2. x2 + 16x + 64

EXAMPLE 2 Make a perfect square trinomial

The trinomial x2 + 16x + c is a perfect square when c = 64. Then x2 + 16x + 64 = (x + 8)(x + 8) = (x + 8)2.

ANSWER

GUIDED PRACTICE for Examples 1 and 2

1. x2 + 6x + 9 = 36.

3 and –9.ANSWER

Solve the equation by finding square roots.

2. x2 – 10x + 25 = 1.

4 and 6.ANSWER

3. x2 – 24x + 144 = 100.

2 and 22.ANSWER

GUIDED PRACTICE for Examples 1 and 2

Find the value of c that makes the expression a perfect square trinomial.Then write the expression as the square of a binomial.

4.

x2 + 14x + c

49 ; (x + 7)2ANSWER

5.

x2 + 22x + c

121 ; (x + 11)2ANSWER

6.

x2 – 9x + c

ANSWER ; (x – )2.814

92