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=8
x equals 8

x=−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 equation is already in the form of a perfect square trinomial.

The expression can be factored as follows:

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

Now, we can solve for \( x \) by taking 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:

x = 8.