Question

Solve for $x$:
$9x-11+\sqrt{3x+7}=-31$

Answer 1

$9x-11+\sqrt{3x+7}=-31$

$\sqrt{3x+7}=-31+11-9x$

$\sqrt{3x+7}=-(9x+20)$

Squaring both sides, we have

${\left(\sqrt{3x+7}\right)}^2={(9x+20)}^2$

$3x+7=81x^2+400+360x$

$\Rightarrow 81x^2+360x+400-3x-7=0$

$\Rightarrow 81x^2+357x+393=0$

From quadratic formula, we get

$x=\frac{-357\pm \sqrt{{\left(357\right)}^2-4\times 393\times 81}}{2\times 81}$

$\Rightarrow x=\frac{-357\pm \sqrt{117}}{162}$

$\therefore$ For $9x-11+\sqrt{3x+7}=-31$-

$x=\frac{-357\pm \sqrt{117}}{162}$