Question 358682
{{{sqrt(x+2)+sqrt(3x+7)=1}}}
{{{sqrt(x+2)=1-sqrt(3x+7)}}}
Square both sides,
{{{x+2=1-2*sqrt(3x+7)+(3x+7)}}}
{{{x+2=2*sqrt(3x+7)+(3x+8)}}}
{{{2*sqrt(3x+7)=-2x-6}}}
{{{4(3x+7)=4x^2+24x+36}}}
{{{12x+28=4x^2+24x+36}}}
{{{4x^2+12x+8=0}}}
{{{x^2+3x+2=0}}}
{{{(x+1)(x+2)=0}}}
Two solutions:
{{{x+1=0}}}
{{{highlight(x=-1)}}}
.
.
.
{{{x+2=0}}}
{{{highlight(x=-2)}}}
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.
.
Verify that both solutions do indeed solve the equation.