Question

Solve for x 6x^2=2x-1

Answer 1

`\displaystyle x=(1\pm i√(5))/(6)`

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

Algebra I

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

Algebra II

• Imaginary Roots: √-1 = i

Explanation:

Step 1: Define

6x² = 2x - 1

Step 2: Rewrite

1. Subtract 2x on both sides: 6x² - 2x = -1
2. Add 1 to both sides: 6x² - 2x + 1 = 0

Step 3: Identify Variables

a = 6

b = -2

c = 1

Step 4: Solve for x

1. Substitute [QF]:
   `\displaystyle x=(2\pm√((-2)^2-4(6)(1)) )/(2(6))`
2. Exponents:
   `\displaystyle x=(2\pm√(4-4(6)(1)) )/(2(6))`
3. Multiplication:
   `\displaystyle x=(2\pm√(4-24) )/(12)`
4. (Square Root) Subtract:
   `\displaystyle x=(2\pm√(-20) )/(12)`
5. Factor:
   `\displaystyle x=(2\pm √(-1) √(20) )/(12)`
6. Simplify:
   `\displaystyle x=(2\pm 2i√(5) )/(12)`
7. Factor GCF:
   `\displaystyle x=(2(1\pm i√(5) ))/(12)`
8. Simplify:
   `\displaystyle x=(1\pm i√(5))/(6)`