%5E2%2B81%3D0.jpeg "(x+8)^2+81=0")
Solving the Equation: (x+8)^2 + 81 = 0
This article will guide you through the steps of solving the equation (x+8)^2 + 81 = 0.
1. Isolate the Squared Term
First, we need to isolate the term with the square on it. We can do this by subtracting 81 from both sides:
(x+8)^2 = -81
2. Take the Square Root
Now, we take the square root of both sides:
√[(x+8)^2] = ±√(-81)
Remember that taking the square root of a number gives us both positive and negative solutions.
3. Simplify and Solve for x
Simplifying, we get:
x+8 = ±9i
Where 'i' is the imaginary unit, defined as √(-1). Now, we isolate 'x' by subtracting 8 from both sides:
x = -8 ± 9i
4. The Solutions
Therefore, the solutions to the equation (x+8)^2 + 81 = 0 are:
- x = -8 + 9i
- x = -8 - 9i
These are complex numbers due to the presence of the imaginary unit 'i'.
Conclusion
We have successfully solved the equation (x+8)^2 + 81 = 0, finding two complex solutions. This example demonstrates how to solve equations involving squared terms, even when the result leads to complex numbers.