<PRE><B>Question 71911</B>
{{{sqrt(3x+7)+sqrt(x+6)=3}}}

{{{sqrt(3x+7)=3-sqrt(x+6)}}}

Square both sides and get:

{{{3x+7=x+15-6sqrt(x+6)}}}

Subtract x+15 from both sides and get:

{{{2x-8=-6sqrt(x+6)}}}

Square both sides again:

{{{4x^2-32x+64=36x+216}}}

{{{4x^2-68x-152=0}}}

Divide by 4:

{{{x^2-17x-38=0}}}

Factor:

(x-19)(x+2)=0

Only one of these is viable. The other is extraneous.

Checking in the original equation, we see x=-2 is the solution.</PRE>