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

Question

.(1 point)
Responses

x=8
x equals 8

x=64
x equals 64

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 can recognize that the left side can be factored.

We see that:

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

Thus, we can rewrite the equation as:

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

Next, we take the square root of both sides:

\[ x - 8 = 0 \]

Solving for \( x \):

\[ x = 8 \]

Therefore, the solution to the equation is \( x = 8 \).

The correct response is:

x=8 (or x equals 8)