Solve the following quadratic equation using the perfect square trinomial pattern: x2−16x+64=0

Question

𝑥
2
−
16
𝑥
+
64
=
0
.(1 point)
Responses

x=−64
𝑥
=
−
64
x equals negative 64

x=8
𝑥
=
8
x equals 8

x=−8
𝑥
=
−
8
x equals negative 8

x=64

Answer 1

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

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

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

Now, we set the factored equation equal to zero:

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

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

\[ x - 8 = 0 \]

Finally, solving for \( x \) gives:

\[ x = 8 \]

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

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