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

1 answer

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.