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Question

Solve the quadratic equation for $x$ by using the quadratic formula method.$$x^{2}+16x+128=0$$

$x^{2}+16x+128=0$

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, $a=1$, $b=16$, and $c=128$

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

$x=\frac{-16\pm \sqrt{256-512}}{2}$

or, $x = \frac{-16\pm \sqrt{-256}}{2}$

or, $x = \frac{-16\pm 16i}{2}$

There are two distinct solutions given by $x = -8+8i$ and $x = -8-8i$