Solve (x+6)1/2= -x
x+6=−x(x+6)2=(−x)2(x+6)=x2x2−x−6=0(x−3)(x+2)=0x−3=0orx+2=0x=3orx=−2Whenx=3;LHS=9=+3RHS=−3LHS≠RHSx=−2;LHS=4=+2RHS=2LHS=RHS∴x=−2\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}x+6(x+6)2(x+6)x2−x−6(x−3)(x+2)x−3=0x=3Whenx=3;LHS=9=+3LHS=RHSx=−2;LHS=4=+2LHS=RHS∴x=−2=−x=(−x)2=x2=0=0orx+2=0orx=−2RHS=−3RHS=2
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