Answer
$x=-1.366$ or $x=0.366$
Work Step by Step
$3^{x^2+x}=\sqrt {3},$
$3^{x^2+x}=3^{\frac{1}{2}},$
$x^2+x=\frac{1}{2},$
$2x^2+2x=1,$
$2x^2+2x-1=0,$
Solving the quadratic equation using the quadratic formula,
$x=\frac{-b \pm \sqrt {b^2-4ac}}{2a},$
$x=\frac{-2 \pm \sqrt {2^2-4(2)(-1)}}{2(2)},$
$x=\frac{-1\pm \sqrt {3}}{2},$
$x=-1.366$ or $x=0.366$
