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

Question

.(1 point)
Responses

x=8
x equals 8

x=64
x equals 64

x=−8
x equals negative 8

x=−64

Answer 1

To solve the quadratic equation \(x^2 - 16x + 64 = 0\) using the perfect square trinomial pattern, we can rewrite it as follows:

Notice that \(x^2 - 16x + 64\) can be factored as \((x - 8)^2\) since:

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

Thus, we can rewrite the equation:

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

Taking the square root of both sides gives:

\[ x - 8 = 0 \]

Solving for \(x\):

\[ x = 8 \]

So the solution is:

x = 8 (or simply "x equals 8").