(x-7)^2=6

2 min read Jun 17, 2024

Solving the Equation (x-7)^2 = 6

This article will guide you through the process of solving the equation (x-7)^2 = 6. This equation involves a squared term, so we'll need to use the square root property to find the solutions.

Step 1: Isolate the Squared Term

The squared term is already isolated on the left side of the equation, so we can proceed to the next step.

Step 2: Take the Square Root of Both Sides

Taking the square root of both sides of the equation eliminates the square:

√[(x-7)^2] = ±√6

This gives us:

x - 7 = ±√6

Step 3: Solve for x

Now we can isolate x by adding 7 to both sides:

x = 7 ±√6

Step 4: Simplify the Solution

This gives us two possible solutions:

x = 7 + √6
x = 7 - √6

Conclusion

Therefore, the solutions to the equation (x-7)^2 = 6 are x = 7 + √6 and x = 7 - √6.