Solve the following quadratic equation using the perfect square trinomial pattern: x2−16x+64=0

Question

.(1 point)
Responses

x=64
x equals 64

x=−8
x equals negative 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 can first recognize that the left side can be factored.

The expression can be rewritten as:

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

To solve for \(x\), we take the square root of both sides:

\[ x - 8 = 0 \]

Adding 8 to both sides gives:

\[ x = 8 \]

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

\[ \boxed{8} \]