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

Question

Responses

x=64
x equals 64

x=−64
x equals negative 64

x=−8
x equals negative 8

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 as follows:

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

So, we rewrite the equation:

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

Next, we take the square root of both sides:

\[ x - 8 = 0 \]

Solving for \(x\), we get:

\[ x = 8 \]

Thus, the solution to the equation is:

\[ \boxed{8} \]

So the correct response is \(x = 8\).