Question

CALCULE; $X-2\sqrt{X}=8$

Answer 1

$x - 2\sqrt{x} = 8 \\ - 2\sqrt{x} = 8 - x \\ \sqrt{x} = \frac{8 - x}{- 2} \\ x = (\frac{8 - x}{- 2})^2 \\ x = \frac{64 - 16x + x^2}{4} \\ 4x = 64 - 16x + x^2 \\ - x^2 + 20x - 64 = 0 \\ a = - 1, b = 20, c = - 64 \\ \\ \Delta = b^2 - 4ac \\ \Delta = 20^2 - 4 \times (- 1) \times (- 64) \\ \Delta = 400 - 256 \\ \Delta = 144 \\ \\ x = \frac{- b \pm \sqrt{\Delta}}{2a} \\ x = \frac{- 20 \pm \sqrt{144}}{2 \times - 1} \\ x = \frac{- 20 \pm 12}{- 2}$

$x = \frac{- 20 + 12}{- 2} = \frac{- 8}{- 2} = 4 \\ x = \frac{- 20 - 12}{- 2} = \frac{- 32}{- 2} = 16$

x = 4, x = 16