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

1 answer

To solve the quadratic equation \( x^2 - 16x + 64 = 0 \) using the perfect square trinomial pattern, we recognize that the expression on the left side can be factored.

The expression \( x^2 - 16x + 64 \) can be rewritten as:

\[ (x - 8)^2 \]

This is because:

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

Now, substituting back into the equation, we have:

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

Next, we 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:

\[ \boxed{8} \]