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

Question

Responses

x=−8
x equals negative 8

x=−64
x equals negative 64

x=64
x equals 64

x=8

Answer 1

To solve the quadratic equation \( x^2 - 16x + 64 = 0 \) using the perfect square trinomial pattern, we first recognize that the left-hand side of the equation can be rewritten as a square of a binomial.

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

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

So we have:

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

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

\[ x - 8 = 0 \]

This gives us:

\[ x = 8 \]

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

x = 8