Solving the Equation (5x2)^2 = 9
This equation involves a squared term, so we'll need to use the square root property to solve for x. Here's a stepbystep breakdown:
1. Take the Square Root of Both Sides

√((5x2)^2) = ±√9
 Remember to include both positive and negative roots since squaring a positive or negative number results in a positive value.
2. Simplify
 5x  2 = ±3
3. Isolate the x Term
 5x = 2 ± 3
4. Solve for x
 x = (2 ± 3) / 5
5. Find the Solutions
 x = (2 + 3) / 5 = 1
 x = (2  3) / 5 = 1/5
Therefore, the solutions to the equation (5x2)^2 = 9 are x = 1 and x = 1/5.
Verification
To verify our solutions, we can substitute them back into the original equation:
 For x = 1:
 (5(1)  2)^2 = (3)^2 = 9
 For x = 1/5:
 (5(1/5)  2)^2 = (3)^2 = 9
Both solutions satisfy the equation, confirming our results.