Question

Find the roots of the equation below.

x2 - 6x + 12 = 0

-3 ± √3
3 ± √3
-3 ± i√3
3 ± i√3

Answer 1

Answer:

$\displaystyle x = 3 \pm i\sqrt{3}$

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

Algebra I

• Factoring
• Standard Form: ax² + bx + c = 0
• Quadratic Formula: $\displaystyle x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$

Algebra II

• Imaginary Numbers: √-1 = i

Step-by-step explanation:

Step 1: Define

x² - 6x + 12 = 0

Step 2: Identify Variables

Compare the quadratic to standard form.

x² - 6x + 12 = 0 ↔ ax² + bx + c = 0

a = 1, b = -6, c = 12

Step 3: Find Roots

1. Substitute in variables [Quadratic Formula]:                                               $\displaystyle x=\frac{-(-6)\pm\sqrt{(-6)^2-4(1)(12)}}{2(1)}$
2. [Quadratic Formula] Simplify:                                                                       $\displaystyle x=\frac{6\pm\sqrt{(-6)^2-4(1)(12)}}{2(1)}$
3. [Quadratic Formula] [√Radical] Evaluate exponents:                                 $\displaystyle x=\frac{6\pm\sqrt{36-4(1)(12)}}{2(1)}$
4. [Quadratic Formula] [√Radical] Multiply:                                                     $\displaystyle x=\frac{6\pm\sqrt{36-48}}{2(1)}$
5. [Quadratic Formula] [√Radical] Subtract:                                                     $\displaystyle x=\frac{6\pm\sqrt{-12}}{2(1)}$
6. [Quadratic Formula] [√Radical] Factor:                                                       $\displaystyle x=\frac{6\pm \sqrt{-1} \cdot \sqrt{12}}{2(1)}$
7. [Quadratic Formula] [√Radicals] Simplify:                                                   $\displaystyle x=\frac{6 \pm 2i\sqrt{3}}{2(1)}$
8. [Quadratic Formula] [Fraction - Denominator] Multiply:                             $\displaystyle x=\frac{6 \pm 2i\sqrt{3}}{2}$
9. [Quadratic Formula] [Fraction - Numerator] Factor:                                   $\displaystyle x=\frac{2(3 \pm i\sqrt{3})}{2}$
10. [Quadratic Formula] [Fraction] Divide:                                                         $\displaystyle x = 3 \pm i\sqrt{3}$