%5E2%3D9.jpeg "(5x-2)^2=9")
Solving the Equation (5x-2)^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 step-by-step breakdown:
1. Take the Square Root of Both Sides
-
√((5x-2)^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 (5x-2)^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.