Question

Solve 2x^2 - 3x + 6 = 0.

Answer 1

`\displaystyle x=(3 \pm i√(39))/(4)`

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
• Factoring
• Quadratic Formula:
  `\displaystyle x=(-b \pm √(b^2-4ac))/(2a)`

Algebra II

• Imaginary Numbers: i = √-1

Explanation:

Step 1: Define

2x² - 3x + 6 = 0

Step 2: Solve for x

1. [Quadratic] Identify Variables [Standard Form]: a = 2, b = -3, c = 6
2. Substitute in variables [Quadratic Formula]:
   `\displaystyle x=(3 \pm √((-3)^2-4(2)(6)))/(2(2))`
3. [√Radical] Evaluate exponents:
   `\displaystyle x=(3 \pm √(9-4(2)(6)))/(2(2))`
4. [√Radical] Multiply:
   `\displaystyle x=(3 \pm √(9-48))/(2(2))`
5. [√Radical] Subtract:
   `\displaystyle x=(3 \pm √(-39))/(2(2))`
6. Multiply:
   `\displaystyle x=(3 \pm √(-39))/(4)`
7. Factor:
   `\displaystyle x=(3 \pm √(-1)√(39))/(4)`
8. Simplify:
   `\displaystyle x=(3 \pm i√(39))/(4)`