# How do you use the quadratic formula to solve 2.5x^2-2.8x=0.4?

Aug 20, 2017

See a solution process below:

#### Explanation:

First, subtract $\textcolor{red}{0.4}$ from each side of the equation to put the equation in standard form while keeping the equation balanced:

$2.5 {x}^{2} - 2.8 x - \textcolor{red}{0.4} = 0.4 - \textcolor{red}{0.4}$

$2.5 {x}^{2} - 2.8 x - 0.4 = 0$

Now we can use the quadratic equation to solve this problem:

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:

$\textcolor{red}{2.5}$ for $\textcolor{red}{a}$

$\textcolor{b l u e}{- 2.8}$ for $\textcolor{b l u e}{b}$

$\textcolor{g r e e n}{- 0.4}$ for $\textcolor{g r e e n}{c}$ gives:

$x = \frac{- \textcolor{b l u e}{\left(- 2.8\right)} \pm \sqrt{{\textcolor{b l u e}{\left(- 2.8\right)}}^{2} - \left(4 \cdot \textcolor{red}{2.5} \cdot \textcolor{g r e e n}{- 0.4}\right)}}{2 \cdot \textcolor{red}{2.5}}$

$x = \frac{2.8 \pm \sqrt{7.84 - 4}}{5}$

$x = \frac{2.8 \pm \sqrt{3.84 - 4}}{5}$