%5E2%3D256.jpeg "(x-4)^2=256")
Solving the Equation (x-4)^2 = 256
This equation involves a squared term, so we'll need to use the square root property to solve for x. Here's how:
1. Take the Square Root of Both Sides
The first step is to isolate the squared term by taking the square root of both sides of the equation:
√[(x-4)^2] = ±√256
Remember that when taking the square root, we need to consider both positive and negative solutions.
2. Simplify
Simplifying both sides, we get:
x - 4 = ±16
3. Isolate x
To find the value of x, we need to isolate it by adding 4 to both sides of the equation:
x = 4 ± 16
4. Calculate the Solutions
This gives us two possible solutions:
- x = 4 + 16 = 20
- x = 4 - 16 = -12
Conclusion
Therefore, the solutions to the equation (x-4)^2 = 256 are x = 20 and x = -12.