Question

Help I cannot figure this question out.

Answer 1

B. x = -1 ± i

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Equality Properties

• Multiplication Property of Equality
• Division Property of Equality
• Addition Property of Equality
• Subtraction Property of Equality

Algebra I

• Standard Form: ax² + bx + c = 0
• Factoring
• Quadratic Formula:
  `\displaystyle x=(-b \pm √(b^2-4ac))/(2a)`

Algebra II

• Imaginary Numbers: √-1 = i

Explanation:

Step 1: Define

x² + 2x = -2

Step 2: Identify Variables

1. Rewrite Quadratic in Standard Form [Addition Property of Equality]: x² + 2x + 2 = 0
2. Break up Quadratic: a = 1, b = 2, c = 2

Step 3: Solve for x

1. Substitute in variables [Quadratic Formula]:
   `\displaystyle x=(-2 \pm √(2^2-4(1)(2)))/(2(1))`
2. [√Radical] Evaluate exponents:
   `\displaystyle x=(-2 \pm √(4-4(1)(2)))/(2(1))`
3. Multiply:
   `\displaystyle x=(-2 \pm √(4-8))/(2)`
4. [√Radical] Subtract:
   `\displaystyle x=(-2 \pm √(-4))/(2)`
5. [√Radical] Factor:
   `\displaystyle x=(-2 \pm √(-1)√(4))/(2)`
6. [√Radicals] Simplify:
   `\displaystyle x=(-2 \pm 2i)/(2)`
7. Factor:
   `\displaystyle x=(2(-1 \pm i))/(2)`
8. Divide:
   `\displaystyle x = -1 \pm i`