Answer
$x=-6$
Work Step by Step
Square both sides and put all terms on one side to create a quadratic equation. Then use trial and error to factor it, and set the values found equal to zero.
$\sqrt {2x+13}=x+7$
$(\sqrt {2x+13})^2=(x+7)^2$
$2x+13=x^2+14x+49$
$x^2+12x+36=0$
$(x+6)(x+6)=0$
$x=-6$
