Question

Solve −3x2 − 4x − 4 = 0.

Answers are

x equals quantity of 2 plus or minus 4i square root of 2 all over 3
x equals quantity of 2 plus or minus 2i square root of 2 all over 3
x equals quantity of negative 2 plus or minus 2i square root of 2 all over 3
x equals quantity of negative 2 plus or minus 4i square root of 2 all over 3

Answer 1

x equals quantity of negative
`2` plus or minus
`2i`i square root of
`2` all over
`3`

Explanation:

we have

`-3x^(2) -4x-4=0`

Rewrite (Multiply by
`-1` both sides)

`3x^(2)+4x+4=0`

The formula to solve a quadratic equation of the form
`ax^(2) +bx+c=0` is equal to

`x=\frac{-b(+/-)\sqrt{b^(2)-4ac}} {2a}`

in this problem we have

`3x^(2)+4x+4=0`

so

`a=3\\b=4\\c=4`

substitute

`x=\frac{-4(+/-)\sqrt{4^(2)-4(3)(4)}} {2(3)}`

`x=\frac{-4(+/-)√(-32)} {6}`

remember that

`i=√(-1)`

`x=\frac{-4(+/-)4i√(2)} {6}`

Simplify

`x=\frac{-2(+/-)2i√(2)} {3}`

`x1=\frac{-2(+)2i√(2)} {3}`

`x2=\frac{-2(-)2i√(2)} {3}`