# How do you solve 0= -2x^2 -8x +9 using the quadratic formula?

Mar 23, 2016

${x}_{1} = - 2 - \frac{\sqrt{34}}{2}$

${x}_{2} = - 2 + \frac{\sqrt{34}}{2}$

#### Explanation:

To simply the computation rewrite equation as:

$- 2 {x}^{2} - 8 x + 9 = 0$

Moltiply both LHS and RHS by $- 1$ to obtain

$2 {x}^{2} + 8 x - 9 = 0$

Now the Quadratic Formula is:

${x}_{1 , 2} = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

with: $a = 2$, $b = 8$ and $c = - 9$

${x}_{1 , 2} = \frac{- 8 \pm \sqrt{64 + 72}}{4} = \frac{- 8 \pm \sqrt{136}}{4} =$
$= - 2 \pm \frac{\sqrt{{2}^{3} \cdot 17}}{4} = - 2 \pm \cancel{2} \frac{\sqrt{2 \cdot 17}}{\cancel{4}} ^ 2 =$
$= - 2 \pm \frac{\sqrt{34}}{2}$

${x}_{1} = - 2 - \frac{\sqrt{34}}{2}$

${x}_{2} = - 2 + \frac{\sqrt{34}}{2}$

graph{2x^2+8x-9 [-7.023, 7.024, -3.51, 3.513]}