Question

The Solving Quadratic Equations Using Patterns Quick Check
Solve the following quadratic equation using the perfect square trinomial pattern: x2-16x+64=0.

Answer 1

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

The equation can be rewritten as:

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

This follows because:

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

Now, we can set the squared term equal to zero:

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

To solve for \( x \), we take the square root of both sides:

\[
x - 8 = 0
\]

Adding 8 to both sides gives:

\[
x = 8
\]

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

\[
\boxed{8}
\]