(x+3)^2+2=-10

Jasonbradley

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Jun 16, 2024

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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 left-hand 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

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

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

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

4. 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