Question

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

Answer 1

`x_1=-2-sqrt(34)/2`

`x_2=-2+sqrt(34)/2`

Explanation:

To simply the computation rewrite equation as:

`-2x^2-8x+9=0`

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

`2x^2+8x-9=0`

Now the Quadratic Formula is:

`x_(1,2)=(-b+-sqrt(b^2-4ac))/(2a)`

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

`x_(1,2)=(-8+-sqrt(64+72))/4=(-8+-sqrt(136))/4=`
`=-2+-sqrt(2^3*17)/4=-2+-cancel(2)sqrt(2*17)/cancel(4)^2=`
`=-2+-sqrt(34)/2`

`x_1=-2-sqrt(34)/2`

`x_2=-2+sqrt(34)/2`

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