Solving the Equation (x + 3)^2 = 9
This equation presents a unique challenge as it involves a square equaling a negative number. Let's break down how to solve it:
Understanding the Problem
 Squares are always nonnegative: The square of any real number (positive, negative, or zero) is always greater than or equal to zero. This means there's no real number that, when squared, results in a negative value.
 Imaginary Numbers: To address this, we need to introduce the concept of imaginary numbers. The imaginary unit, denoted by 'i', is defined as the square root of 1 (i.e., i² = 1).
Solving for x

Isolate the squared term: The equation (x + 3)² = 9 already has the squared term isolated.

Take the square root of both sides: √((x + 3)²) = ±√(9)
Remember: When taking the square root of both sides of an equation, we need to consider both positive and negative solutions. 
Simplify: x + 3 = ±√(9)
x + 3 = ±3i (where 'i' is the imaginary unit) 
Solve for x: x = 3 ± 3i
Solutions
Therefore, the solutions to the equation (x + 3)² = 9 are:
 x = 3 + 3i
 x = 3  3i
These solutions are complex numbers, consisting of a real part (3) and an imaginary part (±3i).