Solving the Equation (y + 8)² = 81
This equation involves a squared term, which means we need to use the square root to solve for 'y'. Here's a step-by-step guide:
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 that when taking the square root, we need to consider both positive and negative solutions:
√(y + 8)² = ±√81
3. Simplify
This simplifies to:
y + 8 = ±9
4. Solve for 'y'
Now, we need to solve for 'y' by subtracting 8 from both sides:
y = -8 ± 9
5. Find the Two Solutions
- y = -8 + 9 = 1
- y = -8 - 9 = -17
Therefore, the solutions to the equation (y + 8)² = 81 are y = 1 and y = -17.