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EleoNora [17]
3 years ago
9

Solve for x. 4x^2 – 2x + 3 = 0

Mathematics
1 answer:
Kipish [7]3 years ago
4 0

Answer:

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

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

<u>Algebra I</u>

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

<u>Algebra II</u>

  • Imaginary Roots: √-1 = i

Step-by-step explanation:

<u>Step 1: Define Equation</u>

4x² - 2x + 3 = 0

<u>Step 2: Identify Variables</u>

a = 4

b = -2

c = 3

<u>Step 3: Solve for </u><em><u>x</u></em>

  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}
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