Solving the Equation: (x+1)^2 = 49
This equation involves a squared term, which means we'll be dealing with a quadratic equation. Let's break down the steps to solve it:
1. Take the Square Root of Both Sides
To isolate the term (x+1), we take the square root of both sides of the equation:
√((x+1)²) = ±√49
This gives us:
x+1 = ±7
2. Solve for x
Now we have two possible solutions, one for the positive and one for the negative square root:

For x+1 = 7 Subtracting 1 from both sides, we get: x = 6

For x+1 = 7 Subtracting 1 from both sides, we get: x = 8
Solutions
Therefore, the solutions to the equation (x+1)² = 49 are x = 6 and x = 8.