Solving the Equation (x+3)^2 + 2 = 10
This article will guide you through solving the equation (x+3)^2 + 2 = 10. We'll explore the steps involved and discuss the nature of the solution.
Understanding the Equation
The equation presents a quadratic expression on the lefthand side. Let's break it down:
 (x+3)^2: This represents the square of the binomial (x+3).
 +2: This is a constant term added to the squared binomial.
The equation is set equal to 10.
Solving for x

Isolate the squared term: Subtract 2 from both sides of the equation: (x+3)^2 = 12

Take the square root of both sides: Remember that taking the square root introduces both positive and negative solutions: x + 3 = ±√(12)

Simplify the square root: √(12) can be simplified as 2√3 * i, where 'i' represents the imaginary unit (√1).

Solve for x: x = 3 ± 2√3 * i
Understanding the Solution
The solutions to the equation are complex numbers. This is because the square root of a negative number results in an imaginary component.
Therefore, the solutions for the equation (x+3)^2 + 2 = 10 are:
 x = 3 + 2√3 * i
 x = 3  2√3 * i