Answer
$x=\pm 2$
Work Step by Step
We are given:
$\sqrt{2x+5}-\sqrt{x+2}=1$
$\sqrt{2x+5}=1+\sqrt{x+2}$
We square both sides:
$(\sqrt{2x+5})^{2}=(1+\sqrt{x+2})^{2}$
$2x+5=1+(x+2)+2\sqrt{x+2}$
$2x+5=3+x+2\sqrt{x+2}$
$x+2=2\sqrt{x+2}$
We square both sides again:
$(x+2)^{2}=(2\sqrt{x+2})^{2}$
$x^{2}+4x+4=4(x+2)$
Distribute 4 then put all terms on the left side of the equation:
$x^{2}+4x+4=4x+8$
$x^2+4x+4-4x-8=0$
$x^{2}-4=0$
And factor:
$(x+2)(x-2)=0$
$(x+2)=0$ or $(x-2)=0$
$x=\pm 2$