Solve the following quadratic equation using the perfect square trinomial pattern: x2−16x+64=0 .(1 point)%0D%0AResponses%0D%0A%0D%0Ax=8%0D%0Ax equals 8%0D%0A%0D%0Ax=64%0D%0Ax equals 64%0D%0A%0D%0Ax=−64%0D%0Ax equals negative 64%0D%0A%0D%0Ax=−8

Answer 1

To solve the quadratic equation \( x^2 - 16x + 64 = 0 \) using the perfect square trinomial pattern, we can rewrite the equation as follows:

Notice that \( x^2 - 16x + 64 \) can be factored as:

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

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

\[ x - 8 = 0 \]

Adding 8 to both sides gives us:

\[ x = 8 \]

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

\[ \boxed{x = 8} \]