Answer :

chetankachana

Answer:

[tex]x = \frac{2 \pm 3\sqrt3}{5}[/tex]

Step-by-step explanation:

Hello!

First, expand the equation:

  • [tex](5x - 2)^2 = 27[/tex]
  • [tex](5x - 2)(5x - 2) = 27[/tex]
  • [tex]25x^2 - 10x - 10x + 4 = 27[/tex]
  • [tex]25x^2 - 20x -23 = 0[/tex]

Standard form of a Quadratic: [tex]ax^2 + bx + c = 0[/tex]

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

Given our Equation: [tex]25x^2 - 20x -23 = 0[/tex]

  • a = 25
  • b = -20
  • c = -23

Solve the Quadratic

  • [tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
  • [tex]x = \frac{20 \pm \sqrt{20^2 - 4(25)(-23)}}{2(25)}[/tex]
  • [tex]x = \frac{20 \pm \sqrt{400 +2300}}{50}[/tex]
  • [tex]x = \frac{20\pm\sqrt{2700}}{50}[/tex]
  • [tex]x = \frac{20\pm30\sqrt3}{50}[/tex]
  • [tex]x = \frac{10(2 \pm3\sqrt3)}{10(5)}[/tex]
  • [tex]x = \frac{\not10(2 \pm3\sqrt3)}{\not10(5)}[/tex]
  • [tex]x = \frac{2 \pm 3\sqrt3}{5}[/tex]

The solutions are [tex]x = \frac{2 + 3\sqrt3}{5}[/tex] and [tex]x = \frac{2 - 3\sqrt3}{5}[/tex].

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