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

Sagot :

Space

Answer:

[tex]\displaystyle x=\frac{1\pm i\sqrt{5}}{6}[/tex]

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: [tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

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