Question

Show how many solutions are in the solution set for 2(x−5)^2+2=20
.(1 point)
Responses

infinitely many
infinitely many

one
one

two
two

zero

Answer 1

To solve the equation \( 2(x - 5)^2 + 2 = 20 \), we can start by simplifying it step by step.

1. Subtract 2 from both sides:
\[
2(x - 5)^2 = 18
\]

2. Divide both sides by 2:
\[
(x - 5)^2 = 9
\]

3. Take the square root of both sides:
\[
x - 5 = 3 \quad \text{or} \quad x - 5 = -3
\]

4. Solve for \( x \):
- From \( x - 5 = 3 \):
\[
x = 8
\]
- From \( x - 5 = -3 \):
\[
x = 2
\]

Thus, we have two solutions: \( x = 8 \) and \( x = 2 \).

Therefore, the answer is **two**.