Question

Solve for x. 4x^2 – 2x + 3 = 0

Answer 1

`x=(1\pm i√(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=(-b\pm√(b^2-4ac) )/(2a)`

Algebra II

• Imaginary Roots: √-1 = i

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=(2\pm√((-2)^2-4(4)(3)) )/(2(4))`
2. Evaluate Exponents:
   `x=(2\pm√(4-4(4)(3)) )/(2(4))`
3. Evaluate Multiplication:
   `x=(2\pm√(4-48) )/(8)`
4. Evaluate Subtraction:
   `x=(2\pm√(-44) )/(8)`
5. Factor Radical:
   `x=(2\pm√(-1) √(44) )/(8)`
6. Simplify Radicals:
   `x=(2\pm 2i√(11) )/(8)`
7. Factor Numerator GCF:
   `x=(2(1\pm i√(11)) )/(8)`
8. Simplify:
   `x=(1\pm i√(11))/(4)`