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

Question

Responses

x=−64
x equals negative 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 recognize that the left side can be written as a square of a binomial.

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

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

Setting this equal to zero gives us:

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

Taking the square root of both sides, we find:

\[ x - 8 = 0 \]

Solving for \( x \), we get:

\[ x = 8 \]

Thus, the solution to the equation is:

\[ \boxed{8} \]