%5E2%2B12%3D41.jpeg "(x-8)^2+12=41")
Solving the Equation: (x-8)^2 + 12 = 41
This article will guide you through the process of solving the equation (x-8)^2 + 12 = 41.
Step 1: Isolate the Squared Term
Begin by isolating the term (x-8)^2 on one side of the equation. To do this, subtract 12 from both sides:
(x-8)^2 + 12 - 12 = 41 - 12 (x-8)^2 = 29
Step 2: Take the Square Root
Now, we need to get rid of the square. Take the square root of both sides of the equation. Remember that taking the square root results in both a positive and negative solution:
√(x-8)^2 = ±√29
This simplifies to: x - 8 = ±√29
Step 3: Solve for x
Finally, isolate x by adding 8 to both sides of the equation:
x - 8 + 8 = ±√29 + 8
Therefore, the solutions for x are:
x = 8 + √29 and x = 8 - √29
Conclusion
By following these steps, we have successfully solved the equation (x-8)^2 + 12 = 41 and found the two possible values for x.