Question

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

x=8
x equals 8

x=64
x equals 64

x=−8
x equals negative 8

x=−64

Answer 1

To solve the quadratic equation \( x^2 - 16x + 64 = 0 \) using the perfect square trinomial pattern, we first recognize that it can be rewritten as:

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

This is because:

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

Now, we set the expression equal to zero:

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

Taking the square root of both sides gives us:

\[
x - 8 = 0
\]

Solving for \( x \) yields:

\[
x = 8
\]

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

**x = 8** (or "x equals 8").