Solve the following quadratic equation using the perfect square trinomial pattern: x2−16x+64=0 .(1 point)

Question

Responses

x=−64
x equals negative 64

x=8
x equals 8

x=−8
x equals negative 8

x=64
x equals 64

Answer 1

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

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

This is because:

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

Setting the equation to 0 gives us:

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

Now, we take the square root of both sides:

\[ x - 8 = 0 \]

Adding 8 to both sides, we find:

\[ x = 8 \]

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

\[ \text{Response: } x = 8 \]