Answer:
[tex]x=\frac{2(1\pm i\sqrt{2} )}{3}[/tex]
General Formulas and Concepts:
Pre-Alg
- Order of Operations: BPEMDAS
Alg I
- Standard Form: ax² + bx + c = 0
- Quadratic Formula: [tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
- √-1 is imaginary number i
Step-by-step explanation:
Step 1: Define
3x² - 4x + 4 = 0
a = 3
b = -4
c = 4
Step 2: Find roots
- Substitute: [tex]x=\frac{-(-4)\pm\sqrt{(-4)^2-4(3)(4)} }{2(3)}[/tex]
- Simplify: [tex]x=\frac{4\pm\sqrt{(-4)^2-4(3)(4)} }{2(3)}[/tex]
- Evaluate: [tex]x=\frac{4\pm\sqrt{16-4(3)(4)} }{2(3)}[/tex]
- Multiply: [tex]x=\frac{4\pm\sqrt{16-48} }{6}[/tex]
- Subtract: [tex]x=\frac{4\pm\sqrt{-32} }{6}[/tex]
- Factor: [tex]x=\frac{4\pm\sqrt{-1} \sqrt{32} }{6}[/tex]
- Simplify: [tex]x=\frac{4\pm4i\sqrt{2} }{6}[/tex]
- Factor: [tex]x=\frac{4(1\pm i\sqrt{2} )}{6}[/tex]
- Simplify: [tex]x=\frac{2(1\pm i\sqrt{2} )}{3}[/tex]
