(y+8)2=81

2 min read Jun 17, 2024

Solving the Equation: (y + 8)² = 81

This equation involves a squared term, which means we'll need to use the square root property to solve for y. Let's break down the steps:

Step 1: Isolate the Squared Term

The squared term is already isolated on the left side of the equation.

Step 2: Take the Square Root of Both Sides

Taking the square root of both sides of the equation helps us get rid of the exponent. Remember that when taking the square root, we have both a positive and a negative solution.

√(y + 8)² = ±√81

Step 3: Simplify

Simplifying both sides gives us:

y + 8 = ±9

Step 4: Solve for y

Now we have two separate equations to solve:

Equation 1: y + 8 = 9
Equation 2: y + 8 = -9

Solving Equation 1:

Subtract 8 from both sides:

y = 1

Solving Equation 2:

Subtract 8 from both sides:

y = -17

Conclusion

Therefore, the solutions to the equation (y + 8)² = 81 are:

y = 1 and y = -17.