(x-5)^4=256

2 min read Jun 17, 2024

Solving the Equation (x-5)^4 = 256

This article will walk you through the steps to solve the equation (x-5)^4 = 256.

Understanding the Equation

The equation presents a fourth-degree polynomial equation. To solve for x, we need to isolate it by taking the fourth root of both sides and then simplifying the resulting expression.

Solving for x

Take the fourth root of both sides: √⁴((x-5)⁴) = √⁴(256)
Simplify: x - 5 = ±4
Isolate x: x = 5 ± 4
Solve for the two possible solutions: x = 5 + 4 = 9 x = 5 - 4 = 1

Solutions

Therefore, the solutions to the equation (x-5)⁴ = 256 are:

x = 9
x = 1

Conclusion

By carefully manipulating the equation and taking the fourth root, we successfully determined the two solutions for x. Remember, when solving equations involving even powers, we need to consider both positive and negative roots.