Question

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

Answer 1

Answer:

$\displaystyle x=\frac{1\pm i\sqrt{5}}{6}$

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: $\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}$

Algebra II

• Imaginary Roots: √-1 = i

Step-by-step 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]:                       $\displaystyle x=\frac{2\pm\sqrt{(-2)^2-4(6)(1)} }{2(6)}$
2. Exponents:                              $\displaystyle x=\frac{2\pm\sqrt{4-4(6)(1)} }{2(6)}$
3. Multiplication:                         $\displaystyle x=\frac{2\pm\sqrt{4-24} }{12}$
4. (Square Root) Subtract:         $\displaystyle x=\frac{2\pm\sqrt{-20} }{12}$
5. Factor:                                    $\displaystyle x=\frac{2\pm \sqrt{-1} \sqrt{20} }{12}$
6. Simplify:                                 $\displaystyle x=\frac{2\pm 2i\sqrt{5} }{12}$
7. Factor GCF:                           $\displaystyle x=\frac{2(1\pm i\sqrt{5} )}{12}$
8. Simplify:                                 $\displaystyle x=\frac{1\pm i\sqrt{5}}{6}$