Question

(5x - 2)^2 = 27 quadratic formula

Answer 1

`x = (2 \pm 3\sqrt3)/(5)`

Explanation:

Hello!

First, expand the equation:

• 
  `(5x - 2)^2 = 27`
• 
  `(5x - 2)(5x - 2) = 27`
• 
  `25x^2 - 10x - 10x + 4 = 27`
• 
  `25x^2 - 20x -23 = 0`

Standard form of a Quadratic:
`ax^2 + bx + c = 0`

Quadratic Formula:
`x = (-b \pm √(b^2 - 4ac))/(2a)`

Given our Equation:
`25x^2 - 20x -23 = 0`

• a = 25
• b = -20
• c = -23

Solve the Quadratic

• 
  `x = (-b \pm √(b^2 - 4ac))/(2a)`
• 
  `x = (20 \pm √(20^2 - 4(25)(-23)))/(2(25))`
• 
  `x = (20 \pm √(400 +2300))/(50)`
• 
  `x = (20\pm√(2700))/(50)`
• 
  `x = (20\pm30\sqrt3)/(50)`
• 
  `x = (10(2 \pm3\sqrt3))/(10(5))`
• 
  `x = (\\ot10(2 \pm3\sqrt3))/(\\ot10(5))`
• 
  `x = (2 \pm 3\sqrt3)/(5)`

The solutions are
`x = (2 + 3\sqrt3)/(5)` and
`x = (2 - 3\sqrt3)/(5)`.