Solving the Equation (x-9)² = 64
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
Taking the square root of both sides will get rid of the square on the left side:
√[(x-9)²] = ±√64
This gives us:
x - 9 = ±8
3. Solve for x
Now we have two separate equations to solve:
- Equation 1: x - 9 = 8
- Equation 2: x - 9 = -8
Solving for x in each equation:
- Equation 1: x = 8 + 9 = 17
- Equation 2: x = -8 + 9 = 1
4. Solutions
Therefore, the solutions to the equation (x-9)² = 64 are x = 17 and x = 1.