Answer
$\left\{\dfrac{-5- \sqrt{13}}{2},\dfrac{-5+ \sqrt{13}}{2}\right\}$
Work Step by Step
The equation is in standard form $ax^2+bx+c=0$.
We have $a=1,b=5$ and $c=3$.
The discriminant is
$=b^2-4ac$
$=(5)^2-4(1)(3)$
$=25-12$
$=13$
Since $13>0$. There are two real solutions.
The quadratic formula is
$x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$
Substitute the values of $a, b, c,$ and the discriminant into the quadratic formula to obtain:
$x=\dfrac{-(5)\pm \sqrt{(13)}}{2(1)}$
Simplify.
$x=\dfrac{-5\pm \sqrt{13}}{2}$
The solution set is $\left\{\dfrac{-5- \sqrt{13}}{2},\dfrac{-5+ \sqrt{13}}{2}\right\}$.
