Question

solve the following quadratic equation using the perfect square trinomial pattern: x^2 - 16x + 64 = 0.
a x = 8
b x = 64
c x = -8
d x = -64

Answer 1

To solve the quadratic equation \( x^2 - 16x + 64 = 0 \) using the perfect square trinomial pattern, we can start by rewriting the quadratic in the form of a perfect square.

Notice that:
\[
x^2 - 16x + 64 = (x - 8)^2
\]
This is because \( (x - 8)(x - 8) = x^2 - 16x + 64 \).

Now, we can set the equation equal to zero:
\[
(x - 8)^2 = 0
\]

Taking the square root of both sides, we get:
\[
x - 8 = 0
\]

Solving for \( x \), we find:
\[
x = 8
\]

Thus, the solution to the quadratic equation \( x^2 - 16x + 64 = 0 \) is
\[
\boxed{8}
\]

Among the options provided:
a) \( x = 8 \) is the correct answer.