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
x equals 8

Answer 1

To solve the quadratic equation \( x^2 - 16x + 64 = 0 \) using the perfect square trinomial pattern, we can rewrite the left side as a squared binomial.

The expression \( x^2 - 16x + 64 \) can be factored as:

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

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

\[ x - 8 = 0 \]

This simplifies to:

\[ x = 8 \]

Thus, the solution to the equation is:

x equals 8.