Question

PLEASE HELP

Solve −3x2 − 4x − 4 = 0.


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` square root of
`2` all over
`3`

Step-by-step 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}`

Answer 2

Answer: The correct solution is option third.

Step-by-step explanation:

The given equation is,

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

The quadratic formula to find the value of x for the equation
`ax^2+bx+c=0` is,

`x=(-b\pm √(b^2-4ac))/(2a)`

The values are,

`a=-3,b=-4,c=-4`

`x=(-(-4)\pm √((-4)^2-4(-3)(-4)))/(2(-3))`

`x=(4\pm √(16-48))/(-6)`

`x=(4\pm √(-32))/(-6)`

Since
`√(-1)=i`,

`x=(4\pm 4i√(2))/(-6)`

`x=(2(2\pm 2i√(2)))/(-6)`

`x=(2\pm 2i√(2))/(-3)`

`x=(-2\pm 2i√(2))/(3)`

Therefore third option is correct.