# How do you solve x^2+3x=12 using the quadratic formula?

May 15, 2017

color(blue)(x=2.275 or color(blue)(x=-5.275 to the nearest 3 decimal places

#### Explanation:

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

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

${x}^{2} + 3 x = 12$

$\therefore {x}^{2} + 3 x - 12 = 0$

$\therefore a = 1 , b = 3 , c = - 12$

$\therefore x = \frac{- \left(3\right) \pm \sqrt{{\left(3\right)}^{2} - 4 \left(1\right) \left(- 12\right)}}{2 \left(1\right)}$

$\therefore x = \frac{- 3 \pm \sqrt{9 + 48}}{2 \left(1\right)}$

$\therefore x = \frac{- 3 \pm \sqrt{57}}{2}$

$\therefore x = \frac{- 3 + 7.549834435}{2}$ or $x = \frac{- 3 - 7.549834435}{2}$

$\therefore x = \frac{4.549834435}{2}$ or $x = \frac{- 10.549834435}{2}$

$\therefore x = 2.2749172175$ or $x = - 5.2749172175$

:.color(blue)(x=2.275 or color(blue)(x=-5.275 to the nearest 3 decimal places

substitute color(blue)(x=2.2749172175

$\therefore {\left(2.2749172175\right)}^{2} + 3 \left(2.2749172175\right) = 12$

$\therefore 5.175248344 + 6.824751651 = 12$

$\therefore 12 = 12$

substitute color(blue)(x=-5.2749172175

$\therefore {\left(- 5.2749172175\right)}^{2} + 3 \left(- 5.2749172175\right) = 12$

$\therefore 27.82475165 - 15.82475165 = 12$

$\therefore 12 = 12$