Question

Solve the following quadratic equation using the perfect square trinomial pattern: x^2 - 16x + 64 = 0

A: x = -64

B: x = -8

C: x = 64

D: x = 8

Answer 1

To solve the quadratic equation \( x^2 - 16x + 64 = 0 \) using the perfect square trinomial pattern, we can recognize that this equation can be expressed in the form \( (x - a)^2 = 0 \).

We can rewrite the equation:

\[
x^2 - 16x + 64 = (x - 8)^2 = 0
\]

Setting the expression equal to zero:

\[
(x - 8)^2 = 0
\]

Taking the square root of both sides gives:

\[
x - 8 = 0
\]

Therefore,

\[
x = 8
\]

So, the solution to the quadratic equation \( x^2 - 16x + 64 = 0 \) is:

\[
\boxed{8}
\]

The correct answer is D: \( x = 8 \).