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

Answer:

x equals quantity of negative $2$ plus or minus $2i$i 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

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

$x=\frac{-4(+/-)\sqrt{-32}} {6}$

remember that

$i=\sqrt{-1}$

$x=\frac{-4(+/-)4i\sqrt{2}} {6}$

Simplify

$x=\frac{-2(+/-)2i\sqrt{2}} {3}$

$x1=\frac{-2(+)2i\sqrt{2}} {3}$

$x2=\frac{-2(-)2i\sqrt{2}} {3}$