Question

Solve the equation by the method of your choice.
left parenthesis 5 x minus 2 right parenthesis squared equals 4

Answer 1

To solve the equation \((5x - 2)^2 = 4\), we can follow these steps:

1. **Take the square root of both sides**:
\[
5x - 2 = \pm 2
\]

2. **Split this into two separate equations**:
- First equation:
\[
5x - 2 = 2
\]
- Second equation:
\[
5x - 2 = -2
\]

3. **Solve the first equation**:
\[
5x - 2 = 2
\]
Adding 2 to both sides:
\[
5x = 4
\]
Now, divide by 5:
\[
x = \frac{4}{5}
\]

4. **Solve the second equation**:
\[
5x - 2 = -2
\]
Adding 2 to both sides:
\[
5x = 0
\]
Now, divide by 5:
\[
x = 0
\]

5. **Conclusion**:
The solutions to the equation \((5x - 2)^2 = 4\) are:
\[
x = \frac{4}{5} \quad \text{and} \quad x = 0
\]