%5E2%3D100.jpeg "(x-5)^2=100")
Solving the Equation (x-5)^2 = 100
This equation involves a squared term, making it a quadratic equation. Let's break down how to solve it:
1. Taking the Square Root
- Isolate the squared term: We already have the squared term isolated on one side of the equation.
- Take the square root of both sides: Remember that taking the square root introduces both positive and negative solutions.
- √(x-5)² = ±√100
- x - 5 = ±10
2. Solving for x
- Separate the equations: We have two possible equations to solve:
- x - 5 = 10
- x - 5 = -10
- Solve for x in each equation:
- Equation 1: x = 10 + 5 = 15
- Equation 2: x = -10 + 5 = -5
Solutions
Therefore, the solutions to the equation (x-5)² = 100 are x = 15 and x = -5.