Question

Solve (2x-3)²= 4x using the quadratic formula

Answer 1

`x = 2 \pm \frac12\sqrt7`

Explanation:

Hello!

Expand the left-hand side of the equation:

• (2x - 3)²
• (2x-3)(2x-3)
• (2x-3)(2x) +(2x-3)(-3)
• 4x² - 6x - 6x + 9
• 4x² - 12x + 9

Create the Equation:

• 4x² - 12x + 9 = 4x
• 4x² - 16x + 9 = 0

Solve using the quadratic formula:

• 
  `x = (-b \pm √(b^2 - 4ac))/(2a)`
• 
  `x = (-(-16) \pm √((-16)^2 - 4(4)(9)))/(2(4))`
• 
  `x = (16 \pm √(256 - 144))/(8)`
• 
  `x = (16 \pm √(112))/(8)`
• 
  `x = (16 \pm 4\sqrt7)/(8)`
• 
  `x = 2 \pm \frac12\sqrt7`

The roots of the equation are
`x = 2 \pm \frac12\sqrt7`