# How do you solve y = 0.04x+ 8.3x + 4.3 using the quadratic formula?

Nov 7, 2017

See a solution process below:

#### Explanation:

Assuming the equation is:

$y = 0.04 {x}^{\textcolor{red}{2}} + 8.3 x + 4.3$

For $\textcolor{red}{a} {x}^{2} + \textcolor{b l u e}{b} x + \textcolor{g r e e n}{c} = 0$, the values of $x$ which are the solutions to the equation are given by:

$x = \frac{- \textcolor{b l u e}{b} \pm \sqrt{{\textcolor{b l u e}{b}}^{2} - \left(4 \textcolor{red}{a} \textcolor{g r e e n}{c}\right)}}{2 \cdot \textcolor{red}{a}}$

Substituting:

$\textcolor{red}{0.04}$ for $\textcolor{red}{a}$

$\textcolor{b l u e}{8.3}$ for $\textcolor{b l u e}{b}$

$\textcolor{g r e e n}{4.3}$ for $\textcolor{g r e e n}{c}$ gives:

$x = \frac{- \textcolor{b l u e}{8.3} \pm \sqrt{{\textcolor{b l u e}{8.3}}^{2} - \left(4 \cdot \textcolor{red}{0.04} \cdot \textcolor{g r e e n}{4.3}\right)}}{2 \cdot \textcolor{red}{0.04}}$

$x = \frac{- \textcolor{b l u e}{8.3} \pm \sqrt{68.89 - 0.688}}{0.08}$

$x = \frac{- 8.3 \pm \sqrt{68.202}}{0.08}$

If it is necessary to get to a single number:

$x = \frac{- 8.3 - 8.258}{0.08}$ and $x = \frac{- 8.3 + 8.258}{0.08}$

$x = - \frac{16.558}{0.08}$ and $x = - \frac{0.042}{0.08}$

$x = - 206.975$ and $x = - - 0.525$

rounded to the nearest thousandth