Question

Solve the following quadratic equation using the perfect square trinomial pattern: x² - 16x + 64 = 0.
(1 point)
x = 8
x = -8
x= 64
x = -64

Answer 1

To solve the quadratic equation \( x^2 - 16x + 64 = 0 \) using the perfect square trinomial pattern, we can rewrite the left side of the equation.

The expression \( x^2 - 16x + 64 \) is a perfect square trinomial. It can be factored as:

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

Next, we set the factored equation equal to zero:

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

Taking the square root of both sides gives us:

\[
x - 8 = 0
\]

Solving for \( x \):

\[
x = 8
\]

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

\[
\boxed{8}
\]