How do you solve (-3-4x)^(1/2)-(-2-2x)^(1/2)=1?

Feb 3, 2018

$x = 3 \pm \frac{\sqrt{29}}{2}$

Explanation:

$\sqrt{- 3 - 4 x} - \sqrt{- 2 - 2 x} = 1$

Square both sides,

$- 3 - 4 x - 2 \sqrt{\left(- 3 - 4 x\right) \left(- 2 - 2 x\right)} - 2 - 2 x = 1$

Multiply And Combine like terms.

$- 6 x - 5 - 2 \sqrt{8 {x}^{2} + 14 x + 6} = 1$

Add $\left[6 x + 5\right]$

$- 2 \sqrt{8 {x}^{2} + 14 x + 6} = 6 x + 6$

Square both Sides again And Multiply.

$32 {x}^{2} + 56 x + 24 = 36 {x}^{2} + 72 x + 36$

Subtract $\left[36 {x}^{2} + 72 x + 36\right]$

$- 4 {x}^{2} - 24 x - 28 = 0$

Use quadratic Formula And simplify again.

$x = \frac{24 \pm \sqrt{576 - 112}}{-} 8 = 3 \pm \frac{\sqrt{29}}{2}$