Show how many solutions are in the solution set for 2(x - 5)² + 2 = 20.

To determine how many solutions are in the solution set for the equation \(2(x - 5)^2 + 2 = 20\), we can start by simplifying it step-by-step.

1. **Subtract 2 from both sides of the equation**:
\[
2(x - 5)^2 + 2 - 2 = 20 - 2
\]
This simplifies to:
\[
2(x - 5)^2 = 18
\]

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

3. **Take the square root of both sides**:
\[
x - 5 = \pm 3
\]

This leads to two equations:

- \(x - 5 = 3\)
- \(x - 5 = -3\)

4. **Solve each equation**:

From \(x - 5 = 3\):
\[
x = 3 + 5 = 8
\]

From \(x - 5 = -3\):
\[
x = -3 + 5 = 2
\]

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

Since we found two distinct solutions, the number of solutions in the solution set is **two**.