Question

How do you solve `-x^2-12x<32` by algebraically?

Answer 1

`x < -8 or x > -4`

Explanation:

`-x^2 - 12 x < 32`
minus with 32,

`-x^2 - 12 x -32 < 0` or `x^2+12 x +32 > 0`

Factorized,

`(-x - 8 )(x + 4 ) < 0` or `(x+8)(x+4) > 0`

                         -oo,              -8,           -4,              +oo

 (-x-8)                               +              -                 -

(x + 4)                               -              -                 +

(-x-8)(x+4)                        -              +                 -

Therefore,
`x < -8 or x > -4`