Solve the following quadratic equation using the perfect square trinomial pattern: x^2 - 16x + 64 = 0

A: x = -64

B: x = -8

C: x = 64

D: x = 8

1 answer

To solve the quadratic equation \( x^2 - 16x + 64 = 0 \) using the perfect square trinomial pattern, we can recognize that this equation can be expressed in the form \( (x - a)^2 = 0 \).

We can rewrite the equation:

\[ x^2 - 16x + 64 = (x - 8)^2 = 0 \]

Setting the expression equal to zero:

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

Taking the square root of both sides gives:

\[ x - 8 = 0 \]

Therefore,

\[ x = 8 \]

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

\[ \boxed{8} \]

The correct answer is D: \( x = 8 \).