%5E2-%3D-256.jpeg "(x+5)^2 = 256")
Solving the Equation: (x+5)^2 = 256
This equation involves a squared term, making it a quadratic equation. Here's how to solve it:
1. Take the Square Root of Both Sides
The first step is to isolate the term inside the parentheses. We can do this by taking the square root of both sides of the equation:
√[(x+5)^2] = ±√256
Remember to include both positive and negative square roots of 256.
2. Simplify
Simplifying the equation, we get:
x + 5 = ±16
3. Solve for x
Now, we have two separate equations to solve:
- Equation 1: x + 5 = 16
- Equation 2: x + 5 = -16
Solving for x in each equation:
- Equation 1: x = 16 - 5 = 11
- Equation 2: x = -16 - 5 = -21
Conclusion
Therefore, the solutions to the equation (x+5)^2 = 256 are x = 11 and x = -21.