Question

What are the values that make x^2 + bx + 64 a perfect square?

Answer 1

16, -16

Explanation:

For a perfect square,

B² - 4AC = 0

b² - 4(1)(64) = 0

b² = 256

b = +/- 16

Answer 2

b = ±16

Explanation:

Normally to find the number we add to make it a perfect square

We take the coefficient of x

b

Divide by 2

b/2

Then square it

(b/2) ^2

In this case, we are adding 64

(b/2) ^2 = 64

Take the square root of each side

sqrt((b/2) ^2) = sqrt(64)

b/2 = ±8

Multiply each side by 2

b/2*2 = ±8 *2

b = ±16