Solve the equation by the method of your choice \( (5 x-2)^{2}=4 \) The solution set is \( \{ \) Simplity 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.) nof 2

To solve the equation \( (5x - 2)^2 = 4 \), follow these steps: 1. **Take the Square Root of Both Sides:** \[ \sqrt{(5x - 2)^2} = \sqrt{4} \] This simplifies to: \[ 5x - 2 = \pm 2 \] 2. **Solve for \( x \) in Each Case:** - **Case 1:** \( 5x - 2 = 2 \) \[ 5x = 2 + 2 \\ 5x = 4 \\ x = \frac{4}{5} \] - **Case 2:** \( 5x - 2 = -2 \) \[ 5x = -2 + 2 \\ 5x = 0 \\ x = 0 \] 3. **Write the Solution Set:** The solutions are \( x = 0 \) and \( x = \frac{4}{5} \). Therefore, the solution set is: \[ \left\{ 0, \frac{4}{5} \right\} \] **Answer:** \(\left\{0, \dfrac{4}{5}\right\}\)