%5E2%3D200.jpeg "(x+4)^2=200")
Solving the Equation: (x + 4)^2 = 200
This equation involves a squared term, meaning we need to use the square root to solve for x. Let's break down the steps:
1. Isolate the squared term:
The squared term is already isolated on the left side of the equation:
(x + 4)^2 = 200
2. Take the square root of both sides:
√(x + 4)^2 = ±√200
- Remember: When taking the square root, we consider both positive and negative solutions.
3. Simplify:
x + 4 = ±√200
- Simplify the radical: √200 = √(100 * 2) = 10√2
4. Isolate x:
x = -4 ± 10√2
5. Solutions:
Therefore, the two solutions for the equation (x + 4)^2 = 200 are:
- x = -4 + 10√2
- x = -4 - 10√2
These are the exact solutions. If you need decimal approximations, you can use a calculator.