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solve each equation 3x^2=80

Sagot :

Chetankachanaidn

Answer:

[tex]x = \frac{4\sqrt{15}}{3}, x = \frac{-4\sqrt{15}}{3}[/tex]

or

[tex]x = \frac{\pm4\sqrt{15}}{3}[/tex]

Step-by-step explanation:

Hello!

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

First, let's convert our equation to standard form of a Quadratic: ax² + bx + c = 0

3x² = 80

3x² - 80 = 0

Note, thats the value of b will be 0, as there is no "bx"

Now, solve:

  • [tex]x = \frac{-(0) \pm \sqrt{(0)^2 - 4(3)(-80)}}{2(3)}[/tex]        Plug in values
  • [tex]x = \frac{\pm\sqrt{960}}{6}[/tex]                              Simplify the radical (Discriminant)
  • [tex]x = \frac{\pm8\sqrt{15}}{6}[/tex]                              Pull out perfect squares
  • [tex]x = \frac{4\sqrt{15}}{3}, x = \frac{-4\sqrt{15}}{3}[/tex]              Reduce factors

 

The solutions are [tex]x = \frac{4\sqrt{15}}{3}, x = \frac{-4\sqrt{15}}{3}[/tex]

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