%5E2%3D18.jpeg "(x-5)^2=18")
Solving the Equation (x-5)^2 = 18
This equation involves a squared term, which means 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: (x - 5)^2 = 18
2. Take the Square Root of Both Sides
Remember that taking the square root introduces both a positive and a negative solution.
√((x - 5)^2) = ±√18
This simplifies to: x - 5 = ±√18
3. Simplify the Radical
√18 can be simplified as √(9 * 2) = 3√2
Therefore, we have: x - 5 = ±3√2
4. Solve for x
Add 5 to both sides: x = 5 ± 3√2
Solutions
This gives us two solutions:
- x = 5 + 3√2
- x = 5 - 3√2
These are the exact solutions to the equation (x-5)^2 = 18. You can approximate these solutions using a calculator if needed.