(k+1)2=9

Jasonbradley

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Jun 16, 2024

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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

1. 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.

2. Simplify:

   • k + 1 = ±3

3. Isolate k:

   • k = ±3 - 1

4. 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.