# How do you solve x^2+4x+3=0 using the quadratic formula?

Jul 22, 2017

$- 1 \text{ or } - 3$

#### Explanation:

$a {x}^{2} + b x + c = 0$

the formula for the roots is

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

$\left(1\right) \text{ }$ Identify the values for a,b,&" "c

${x}^{2} + 4 x + 3 = 0$

cmp

$a {x}^{2} + b x + c = 0$

$\textcolor{red}{a = 1}$

$\textcolor{b l u e}{b = 4}$

$\textcolor{g r e e n}{c = 3}$

$\left(2\right) \text{ }$Substitute these numbers into eh formula

$x = \frac{\textcolor{b l u e}{- 4} \pm \sqrt{\textcolor{b l u e}{{4}^{2}} - \left(4 \times \textcolor{red}{1} \times \textcolor{g r e e n}{3}\right)}}{2 \times \textcolor{red}{1}}$

$\left(3\right) \text{ }$Carefully proceed and do the calculations

$x = \frac{- 4 \pm \sqrt{16 - 12}}{2}$

$x = \frac{- 4 \pm \sqrt{4}}{2}$

$x = \frac{- 4 \pm 2}{2}$

now calculate the two separate solutions

${x}_{1} = \frac{- 4 + 2}{2} = - \frac{2}{2} = - 1$

${x}_{2} = \frac{- 4 - 2}{2} = - \frac{6}{2} = - 3$