# Question #64b2f

Mar 23, 2016

$x = 1.3083 \pm 0.6324 i$

#### Explanation:

To solve for $x$ in the quadratic equation

$y = - 0.7428 {x}^{2} + 1.9437 x - 1.569$

Use the quadratic formula, which solves for $x$ in the quadratic equation

$y = a {x}^{2} + b x + c$

where

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

In the given quadratic, we see that

$\left\{\begin{matrix}a = - 0.7428 \\ b = 1.9437 \\ c = - 1.569\end{matrix}\right.$

Thus,

$x = \frac{- 1.9437 \pm \sqrt{{1.9437}^{2} - 4 \left(- 0.7428\right) \left(- 1.569\right)}}{2 \left(- 0.7428\right)}$

$x = \frac{- 1.9437 \pm \sqrt{- 0.8838}}{- 1.4856}$

Bring the negative out as $i$. Take the square root of $0.8838$.

$x = \frac{- 1.9437}{- 1.4865} \pm \frac{0.9401}{- 1.4856} i$

$x = 1.3083 \pm 0.6324 i$