(x-9)^2+26=31

2 min read Jun 17, 2024

Solving the Equation: (x-9)^2 + 26 = 31

This article will guide you through the process of solving the equation (x-9)^2 + 26 = 31. We'll break down the steps and provide explanations to help you understand the solution.

1. Isolate the Squared Term

First, we need to isolate the term (x-9)^2. To do this, we subtract 26 from both sides of the equation:

(x-9)^2 + 26 - 26 = 31 - 26

This simplifies to:

(x-9)^2 = 5

2. Take the Square Root of Both Sides

Now, we take the square root of both sides of the equation to get rid of the square:

√(x-9)^2 = ±√5

This gives us:

x - 9 = ±√5

3. Solve for x

Finally, we solve for x by adding 9 to both sides of the equation:

x - 9 + 9 = ±√5 + 9

This leaves us with:

x = 9 ± √5

Conclusion

Therefore, the solutions to the equation (x-9)^2 + 26 = 31 are:

x = 9 + √5

and

x = 9 - √5

By following these steps, we have successfully solved the equation and found the two possible values for x.