%5E2%3D81.jpeg "(x+3)^2=81")
Solving the Equation (x + 3)^2 = 81
This equation involves a squared term, so we'll need to use the square root property to solve for x. Here's how:
1. Isolate the Squared Term
The squared term is already isolated on the left side of the equation.
2. Take the Square Root of Both Sides
Remember to consider both positive and negative square roots:
√(x + 3)^2 = ±√81
3. Simplify
This simplifies to:
x + 3 = ±9
4. Solve for x
We have two possible solutions:
-
Case 1: x + 3 = 9
- Subtract 3 from both sides: x = 6
-
Case 2: x + 3 = -9
- Subtract 3 from both sides: x = -12
5. Verify the Solutions
We can plug each solution back into the original equation to verify they work:
- For x = 6: (6 + 3)^2 = 9^2 = 81 (This solution works)
- For x = -12: (-12 + 3)^2 = (-9)^2 = 81 (This solution also works)
Conclusion
Therefore, the solutions to the equation (x + 3)^2 = 81 are x = 6 and x = -12.