Question

Solve for x. 4x^2 – 2x + 3 = 0

Answer 1

Answer:

$x=\frac{1\pm i\sqrt{11}}{4}$

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

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

Algebra II

• Imaginary Roots: √-1 = i

Step-by-step explanation:

Step 1: Define Equation

4x² - 2x + 3 = 0

Step 2: Identify Variables

a = 4

b = -2

c = 3

Step 3: Solve for x

1. Substitute [Quad Formula]:                    $x=\frac{2\pm\sqrt{(-2)^2-4(4)(3)} }{2(4)}$
2. Evaluate Exponents:                               $x=\frac{2\pm\sqrt{4-4(4)(3)} }{2(4)}$
3. Evaluate Multiplication:                          $x=\frac{2\pm\sqrt{4-48} }{8}$
4. Evaluate Subtraction:                             $x=\frac{2\pm\sqrt{-44} }{8}$
5. Factor Radical:                                        $x=\frac{2\pm\sqrt{-1} \sqrt{44} }{8}$
6. Simplify Radicals:                                   $x=\frac{2\pm 2i\sqrt{11} }{8}$
7. Factor Numerator GCF:                         $x=\frac{2(1\pm i\sqrt{11}) }{8}$
8. Simplify:                                                  $x=\frac{1\pm i\sqrt{11}}{4}$