(x-4)^2=11

2 min read Jun 17, 2024

Solving the Equation (x-4)^2 = 11

This article will guide you through solving the equation (x-4)^2 = 11. We'll use the concept of square roots to find the solutions.

Understanding the Equation

The equation (x-4)^2 = 11 represents a quadratic equation. This means that the highest power of the variable 'x' is 2. To solve for 'x', we need to isolate it.

Solving for 'x'

Take the square root of both sides: The first step is to get rid of the square. We do this by taking the square root of both sides of the equation. Remember, taking the square root introduces both positive and negative solutions.
```
√((x-4)^2) = ±√11
```
Simplify: The square root of (x-4)^2 is simply (x-4), and we are left with:
```
x-4 = ±√11
```
Isolate 'x': To isolate 'x', add 4 to both sides of the equation:
```
x = 4 ±√11
```

The Solutions

Therefore, the solutions to the equation (x-4)^2 = 11 are:

x = 4 + √11
x = 4 - √11

Conclusion

By following these steps, we have successfully solved the equation (x-4)^2 = 11 and found its two solutions. Remember that when solving quadratic equations, you may encounter multiple solutions due to the square root operation.