%5E2-2%3D-5.jpeg "(x-3)^2-2=-5")
Solving the Equation: (x - 3)^2 - 2 = -5
This article will guide you through the steps to solve the equation (x - 3)^2 - 2 = -5.
Step 1: Isolate the Squared Term
First, we need to isolate the term with the squared variable. To do this, we'll add 2 to both sides of the equation:
(x - 3)^2 - 2 + 2 = -5 + 2
This simplifies to:
(x - 3)^2 = -3
Step 2: Take the Square Root
Now, we need to get rid of the square. To do this, we take the square root of both sides of the equation. Remember that taking the square root results in both positive and negative solutions:
√[(x - 3)^2] = ±√(-3)
This simplifies to:
x - 3 = ±√(-3)
Step 3: Simplify and Solve for x
We know that the square root of a negative number is imaginary. Therefore, we can express √(-3) as √3 * i, where 'i' is the imaginary unit (i = √-1).
Now, we have:
x - 3 = ±√3 * i
Finally, add 3 to both sides to isolate x:
x = 3 ±√3 * i
Conclusion
The solutions to the equation (x - 3)^2 - 2 = -5 are x = 3 + √3 * i and x = 3 - √3 * i. These are complex solutions, meaning they involve the imaginary unit 'i'.