Solve Quadratic Equations(Complex Solutions)

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**Answer**

$x^{2}+4x+85=0$

The solutions of a *quadratic equation* $ax^2+bx + c = 0$ are given by$$x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$$

In this *quadratic equation*, $a=1$, $b=4$, and $c=85$

Substituting these values of $a$, $b$ and $c$ in the above formula, we get

$x=\frac{-4\pm \sqrt{16-340}}{2}$

or, $x = \frac{-4\pm \sqrt{-324}}{2}$

or, $x = \frac{-4\pm 18i}{2}$

There are two distinct solutions given by $x = -2+9i$ and $x = -2-9i$