(x-7)^2+5=41

2 min read Jun 17, 2024

Solving the Equation (x-7)^2 + 5 = 41

This article will guide you through the steps of solving the equation (x-7)^2 + 5 = 41.

1. Isolate the Squared Term

Our first step is to isolate the term containing the squared expression, (x-7)^2. We can do this by subtracting 5 from both sides of the equation:

(x-7)^2 + 5 - 5 = 41 - 5

This simplifies to:

(x-7)^2 = 36

2. Take the Square Root of Both Sides

Now we can get rid of the square by taking the square root of both sides of the equation. Remember that taking the square root can result in both a positive and negative solution:

√(x-7)^2 = ±√36

This simplifies to:

(x-7) = ±6

3. Solve for x

We now have two separate equations to solve:

x-7 = 6
x-7 = -6

Solving the first equation, we add 7 to both sides:

x - 7 + 7 = 6 + 7

x = 13

Solving the second equation, we also add 7 to both sides:

x - 7 + 7 = -6 + 7

x = 1

Conclusion

Therefore, the solutions to the equation (x-7)^2 + 5 = 41 are x = 13 and x = 1.