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Use the quadratic formula to solve for x. 3x2 = 8x-1 Round your answer to the nearest hundredth. If there is more than one solution, separate them with commas. = 0 X $ ?​

Respuesta :

Space

Answer:

[tex]x \approx 0.13, 2.54[/tex]

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: [tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

Step-by-step explanation:

Step 1: Define

3x² = 8x - 1

Step 2: Rewrite

Put equation in Standard Form

  1. Subtract 8x on both sides:                    3x² - 8x = -1
  2. Add 1 to both sides:                               3x² - 8x + 1 = 0

Step 3: Identify Variables

a = 3

b = -8

c = 1

Step 4: Solve for x

  1. Substitute [Quad Formula]:                    [tex]x=\frac{8\pm\sqrt{(-8)^2-4(3)(1)} }{2(3)}[/tex]
  2. Evaluate Exponents:                               [tex]x=\frac{8\pm\sqrt{64-4(3)(1)} }{2(3)}[/tex]
  3. Multiplication:                                          [tex]x=\frac{8\pm\sqrt{64-12} }{6}[/tex]
  4. Subtraction:                                             [tex]x=\frac{8\pm\sqrt{52} }{6}[/tex]
  5. Simplify Radical:                                      [tex]x=\frac{8\pm2\sqrt{13} }{6}[/tex]
  6. Factor GCF:                                             [tex]x=\frac{2(4\pm\sqrt{13}) }{6}[/tex]
  7. Simplify Fraction:                                    [tex]x=\frac{4\pm\sqrt{13}}{3}[/tex]
  8. Evaluate:                                                  [tex]x=0.131483, 2.53518[/tex]
  9. Round:                                                     [tex]x \approx 0.13, 2.54[/tex]

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