Solving for k in the Equation (k+1)² = 9
This article will guide you through the process of solving for k in the equation (k+1)² = 9. We will break down the steps and explain the reasoning behind each one.
Understanding the Equation
The equation (k+1)² = 9 represents a quadratic equation. This means that the unknown variable k appears raised to the power of 2. To solve for k, we need to isolate it.
Solving the Equation

Take the square root of both sides:
 √(k+1)² = ±√9
 This step eliminates the square on the left side of the equation. Remember that taking the square root can result in both a positive and negative value.

Simplify:
 k + 1 = ±3

Isolate k:
 k = ±3  1

Calculate the two possible solutions:
 k = 3  1 = 2
 k = 3  1 = 4
Verifying the Solutions
To confirm that our solutions are correct, we can substitute them back into the original equation:
 For k = 2: (2 + 1)² = 3² = 9. This is true.
 For k = 4: (4 + 1)² = (3)² = 9. This is also true.
Conclusion
Therefore, the solutions to the equation (k+1)² = 9 are k = 2 and k = 4.