Question

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

x=−64
x equals negative 64

x=−8
x equals negative 8

x=8
x equals 8

x=64
x equals 64

Answer 1

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

The equation can be rewritten as:

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

This is because \( (x - 8)(x - 8) = x^2 - 16x + 64 \).

Now, we set the equation 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 \( x = 8 \).

The response is:
**x=8**