Answer:
[tex]x=-2\pm 3i[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Algebra I
- Standard Form: ax² + bx + c = 0
- Quadratic Formula: [tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
Algebra II
- Imaginary Numbers: √-1 = i
Step-by-step explanation:
Step 1: Define
x² + 4x + 13 = 0
Step 2: Identify Variables
a = 1
b = 4
c = 13
Step 3: Find roots
- Substitute: [tex]x=\frac{-4\pm\sqrt{4^2-4(1)(13)} }{2(1)}[/tex]
- Exponents: [tex]x=\frac{-4\pm\sqrt{16-4(1)(13)} }{2(1)}[/tex]
- Multiply: [tex]x=\frac{-4\pm\sqrt{16-52} }{2}[/tex]
- Subtract: [tex]x=\frac{-4\pm\sqrt{-36} }{2}[/tex]
- Factor: [tex]x=\frac{-4\pm\sqrt{-1}\sqrt{36} }{2}[/tex]
- Evaluate: [tex]x=\frac{-4\pm 6i }{2}[/tex]
- Factor: [tex]x=\frac{2(-2\pm 3i) }{2}[/tex]
- Divide: [tex]x=-2\pm 3i[/tex]
