How do you solve ${(- 3 - 4 x)}^{\frac{1}{2}} - {(- 2 - 2 x)}^{\frac{1}{2}} = 1$ $(-3-4x)^(1/2)-(-2-2x)^(1/2)=1$ ?

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Answer 1 · 2018-02-03T23:52:23

$x = 3 \pm \frac{\sqrt{29}}{2}$ $x=3+-sqrt(29)/2$

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

Square both sides,

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

Multiply And Combine like terms.

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

Add $[6 x + 5]$ $[6x+5]$

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

Square both Sides again And Multiply.

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

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

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

Use quadratic Formula And simplify again.

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

How do you solve (−3−4x)12−(−2−2x)12=1(-3-4x)^(1/2)-(-2-2x)^(1/2)=1?