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Sagot :
Answer:
[tex]\displaystyle x=\frac{1\pm i\sqrt{5}}{6}[/tex]
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 = 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
- Subtract 2x on both sides: 6x² - 2x = -1
- Add 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]: [tex]\displaystyle x=\frac{2\pm\sqrt{(-2)^2-4(6)(1)} }{2(6)}[/tex]
- Exponents: [tex]\displaystyle x=\frac{2\pm\sqrt{4-4(6)(1)} }{2(6)}[/tex]
- Multiplication: [tex]\displaystyle x=\frac{2\pm\sqrt{4-24} }{12}[/tex]
- (Square Root) Subtract: [tex]\displaystyle x=\frac{2\pm\sqrt{-20} }{12}[/tex]
- Factor: [tex]\displaystyle x=\frac{2\pm \sqrt{-1} \sqrt{20} }{12}[/tex]
- Simplify: [tex]\displaystyle x=\frac{2\pm 2i\sqrt{5} }{12}[/tex]
- Factor GCF: [tex]\displaystyle x=\frac{2(1\pm i\sqrt{5} )}{12}[/tex]
- Simplify: [tex]\displaystyle x=\frac{1\pm i\sqrt{5}}{6}[/tex]
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