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

1 Answer

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Answer:


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

User Nishan Dhungana
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