Solve for x using the quadratic formula. x^(2) +4x+13=0

Question

Solve for x using the quadratic formula.


`x^(2) +4x+13=0`

Answer 1

`x=-2\pm 3i`

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

Algebra I

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

Algebra II

• Imaginary Numbers: √-1 = i

Explanation:

Step 1: Define

x² + 4x + 13 = 0

Step 2: Identify Variables

a = 1

b = 4

c = 13

Step 3: Find roots

1. Substitute:
   `x=(-4\pm√(4^2-4(1)(13)) )/(2(1))`
2. Exponents:
   `x=(-4\pm√(16-4(1)(13)) )/(2(1))`
3. Multiply:
   `x=(-4\pm√(16-52) )/(2)`
4. Subtract:
   `x=(-4\pm√(-36) )/(2)`
5. Factor:
   `x=(-4\pm√(-1)√(36) )/(2)`
6. Evaluate:
   `x=(-4\pm 6i )/(2)`
7. Factor:
   `x=(2(-2\pm 3i) )/(2)`
8. Divide:
   `x=-2\pm 3i`