I assume that the question was about
[tex]\sqrt{x+2}+\sqrt{x+9}=7[/tex]
First of all, square both sides:
[tex](x+2)+(x+9)+2\sqrt{x+2}\sqrt{x+9}=49[/tex]
Simplify and leave only the roots at the left hand side:
[tex]\sqrt{x+2}\sqrt{x+9}=-x+19[/tex]
Square again:
[tex]x^2+11x+18=x^2-38x+361[/tex]
Simplify/rearrange:
[tex]49x=343 \iff x=\dfrac{343}{49}=7[/tex]
