# How do you solve using the quadratic formula 2x^2 + 5x = -3?

Jun 12, 2017

#### Answer:

See a solution process below:

#### Explanation:

First, put this equation in standard form:

$2 {x}^{2} + 5 x + \textcolor{red}{3} = - 3 + \textcolor{red}{3}$

$2 {x}^{2} + 5 x + 3 = 0$

The quadratic formula states:

For $a {x}^{2} + b x + c = 0$, the values of $x$ which are the solutions to the equation are given by:

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

Substituting $2$ for $a$; $5$ for $b$ and $3$ for $c$ gives:

$x = \frac{- 5 \pm \sqrt{{5}^{2} - \left(4 \cdot 2 \cdot 3\right)}}{2 \cdot 2}$

$x = \frac{- 5 \pm \sqrt{25 - 24}}{4}$

$x = \frac{- 5 \pm \sqrt{1}}{4}$

$x = \frac{- 5 \pm 1}{4}$

$x = \frac{- 5 - 1}{4}$ or $x = \frac{- 5 + 1}{4}$

$x = - \frac{6}{4}$ or $x = - \frac{4}{4}$

$x = - \frac{3}{2}$ or $x = - 1$