Question

Solve using the quadratic formula
2x^2+x+67=0

Answer 1

`\displaystyle x=(-1 \pm i√(535))/(2)`

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

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

Algebra II

• Imaginary Root i = √-1

Explanation:

Step 1: Define

Identify

2x² + x + 67 = 0

a = 2

b = 1

c = 67

Step 2: Solve for x

1. Substitute in variables [Quadratic Formula]:
   `\displaystyle x=(-1 \pm √(1^2-4(2)(67)))/(2(1))`
2. Multiply:
   `\displaystyle x=(-1 \pm √(1^2-4(2)(67)))/(2)`
3. [√Radical] Evaluate exponents:
   `\displaystyle x=(-1 \pm √(1-4(2)(67)))/(2)`
4. [√Radical] Multiply:
   `\displaystyle x=(-1 \pm √(1-536))/(2)`
5. [√Radical] Subtract:
   `\displaystyle x=(-1 \pm √(-535))/(2)`
6. [√Radical] Simplify:
   `\displaystyle x=(-1 \pm i√(535))/(2)`