# How do you solve 2x^2+9x+9=0?

May 20, 2017

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

x=(-9+-sqrt(9^2-4xx2xx9))/(2xx2

x=(-9+-sqrt(81-72))/(4

x=(-9+-sqrt(9))/(4

x=(-9+-3)/(4

x=(-9+3)/(4

x=(-9-3)/(4

x=(-6)/(4

x=(-12)/(4

$x = - \frac{3}{2} , - 3$

#### Explanation:

Plug the values into the Quadratic Formula

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

May 20, 2017

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

#### Explanation:

$\text{'splitting' the middle term to give}$

$2 {x}^{2} + 6 x + 3 x + 9 = 0$

$\text{taking out a common factor from each 'pair'}$

$\textcolor{red}{2 x} \left(x + 3\right) \textcolor{red}{+ 3} \left(x + 3\right) = 0$

$\text{taking out the common factor } \left(x + 3\right)$

$\left(x + 3\right) \left(\textcolor{red}{2 x + 3}\right) = 0$

$\text{equate each factor to zero}$

$x + 3 = 0 \to x = - 3$

$2 x + 3 = 0 \to x = - \frac{3}{2}$

$\textcolor{b l u e}{\text{As a check}}$

$2 {\left(- 3\right)}^{2} + 9 \left(- 3\right) + 9 = 18 - 27 + 9 = 0 \rightarrow \text{ True}$

$2 {\left(- \frac{3}{2}\right)}^{2} + 9 \left(- \frac{3}{2}\right) + 9 = \frac{9}{2} - \frac{27}{2} + \frac{18}{2} = 0$

$\Rightarrow x = - 3 \text{ or " x=-3/2" are the solutions}$