Question

Solve the following quadratic equation using the perfect square trinomial pattern: x^2−16x+64=0 .(1 point)
Responses

x=64
x equals 64

x=8
x equals 8

x=−64
x equals negative 64

x=−8

Answer 1

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

The general form of a perfect square trinomial is \( (x - a)^2 = 0 \). In this case, we can see that:

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

So we rewrite the equation:

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

Now, we can take the square root of both sides:

\[
x - 8 = 0
\]

Solving for \( x \):

\[
x = 8
\]

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

**x = 8**

So the correct response is:

**x=8**