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

zero
zero

two
two

Answer 1

Let's solve the equation \( 2(x - 5)^2 + 2 = 20 \).

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

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

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

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

Thus, the two solutions are \( x = 8 \) and \( x = 2 \).

Therefore, the number of solutions in the solution set is **two**.