Answer
$\left \{\frac{3}{2} \pm \frac{ i}{2}\right \}$.
Work Step by Step
The standard form the quadratic equation is
$\Rightarrow ax^2+bx+c=0 $
The solutions for the standard form can be calculated with the Quadratic Formula
$\Rightarrow x=\frac{−b\pm \sqrt{b^2−4ac}}{2a}$
Compare the given equation with the standard form to identify $a$, $b$, $c$.
$a=2,b=-6$ and $ c=5$
The solutions are
$\Rightarrow x=\frac{−(-6)\pm \sqrt{(-6)^2−4(2)(5)}}{2(2)}$
Simplify.
$\Rightarrow x=\frac{6\pm \sqrt{36−40}}{4}$
$\Rightarrow x=\frac{6\pm \sqrt{−4}}{4}$
$\Rightarrow x=\frac{6\pm \sqrt{−1 \cdot 2^2}}{4}$
$\Rightarrow x=\frac{6\pm 2\sqrt{−1 }}{4}$
Factor out 2.
$\Rightarrow x=\frac{2(3\pm \sqrt{−1 })}{4}$
Cancel common term 2.
$\Rightarrow x=\frac{3\pm \sqrt{−1 }}{2}$
Use $\sqrt{-1}=i$
$\Rightarrow x=\frac{3\pm i}{2}$
$\Rightarrow x=\frac{3}{2} \pm \frac{ i}{2}$
The solution set is $\left \{\frac{3}{2} \pm \frac{ i}{2}\right \}$.
