Answer to Question #169191 in Algebra for william

Question

Solve (x+6)^1/2= -x

Answer 1

$\qquad\qquad \begin{aligned} \sqrt{x+6}&= -x\qquad\\ (\sqrt{x+6})^2&=(-x)^2\\ (x+6)&=x^2\\ x^2-x-6&=0\\ (x-3)(x+2)&=0\\ \\ x-3=0\qquad&{or}\qquad{x+2=0}\\ x=3\qquad&{or}\qquad{x=- 2}\\\\ When \qquad{x=3};\qquad{\small LHS=\sqrt{9}=+3}\qquad &\small RHS=-3\\ \small LHS\neq RHS\\ x=-2;\qquad{\small LHS=\sqrt{4}=+2}\qquad& \small RHS=2\\ \small LHS=RHS\\\\ \therefore\qquad \bold{x=-2} \end{aligned}$