Asked by Landon Sharp
Solve the following quadratic equation using the perfect square trinomial pattern: x2−16x+64=0
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
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
Answers
Answered by
GPT-4o mini
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:
\[
\text{Response: } x = 8
\]
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:
\[
\text{Response: } x = 8
\]