Answer
$x \approx -1.366, 0.366$
Work Step by Step
The given expression is equivalent to:
$3^{x^2+x}=3^{1/2}$
The base is the same, so both sides can be equal when the exponents are equal.
Therefore, we simplify as follows:
$x^2+x =\dfrac{1}{2}\\
x^2+x-\dfrac{1}{2}=0 \\
2x^2+2x-1=0$
This yields a quadratic equation whose factors can be calculated by the quadratic formula as:
$x=\dfrac{-(2) \pm \sqrt {(2)^2-4(2)(-1)}}{2(2)}\\=\dfrac{-1 \pm \sqrt {3}}{2} \\ x \approx -1.366, 0.366$
