Question

Solve the equation by the method of your choice.
left parenthesis 5 x minus 1 right parenthesis squared equals 1
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Part 1
The solution set is StartSet nothing EndSet
  
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​(Simplify your answer. Type an exact​ answer, using radicals and i as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as​ needed.)

Answer 1

To solve the equation \( (5x - 1)^2 = 1 \), we start by taking the square root of both sides. This gives us two cases to consider:

1. \( 5x - 1 = 1 \)
2. \( 5x - 1 = -1 \)

### Case 1: \( 5x - 1 = 1 \)

To solve for \( x \):
\[
5x - 1 = 1
\]
Add 1 to both sides:
\[
5x = 2
\]
Now divide by 5:
\[
x = \frac{2}{5}
\]

### Case 2: \( 5x - 1 = -1 \)

To solve for \( x \):
\[
5x - 1 = -1
\]
Add 1 to both sides:
\[
5x = 0
\]
Now divide by 5:
\[
x = 0
\]

### Solution Set

The solutions from both cases are:
- From Case 1: \( x = \frac{2}{5} \)
- From Case 2: \( x = 0 \)

Thus, the solution set is:
\[
\left\{ 0, \frac{2}{5} \right\}
\]

So, the final answer is \( \left\{ 0, \frac{2}{5} \right\} \).