Question

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

Answer 1

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

Recall that a perfect square trinomial is of the form \((a - b)^2 = a^2 - 2ab + b^2\).

In your equation \(x^2 - 16x + 64\):

1. **Identify \(a\)**: The coefficient of \(x\) is \(-16\), so half of that is \(-8\).
2. **Identify \(b^2\)**: The last term is \(64\), which is \(8^2\).

This means that the equation can be rewritten as:

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

Now, we can take the square root of both sides:

\[
x - 8 = 0
\]

Solving for \(x\), we get:

\[
x = 8
\]

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

\[
\boxed{8}
\]