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

Solve for x 6x^2=2x-1 - id622110135538, studyoverload

Ответ:

GgRed

16.03.2022

Mathematics

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

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Equality Properties

Algebra I

Standard Form: ax² + bx + c = 0Quadratic 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

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

Step 3: Identify Variables

a = 6

b = -2

c = 1

Step 4: Solve for x

Substitute [QF]: $\displaystyle x=\frac{2\pm\sqrt{(-2)^2-4(6)(1)} }{2(6)}$ Exponents: $\displaystyle x=\frac{2\pm\sqrt{4-4(6)(1)} }{2(6)}$ Multiplication: $\displaystyle x=\frac{2\pm\sqrt{4-24} }{12}$ (Square Root) Subtract: $\displaystyle x=\frac{2\pm\sqrt{-20} }{12}$ Factor: $\displaystyle x=\frac{2\pm \sqrt{-1} \sqrt{20} }{12}$ Simplify: $\displaystyle x=\frac{2\pm 2i\sqrt{5} }{12}$ Factor GCF: $\displaystyle x=\frac{2(1\pm i\sqrt{5} )}{12}$ Simplify: $\displaystyle x=\frac{1\pm i\sqrt{5}}{6}$

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

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