Question

Solve -3x2 - 4x - 4 = 0.

Answer 1

well you have to find the factors of that equation, you do that by finding numbers that you can either mulyiply add or subtract to get the first, middle and last term ok so lets start. the number 3 only has 2 numbers that ca be multiplied to get it this are 1 and 3 so we already know that one side will have a 1 and an X and the other will have a 3 and an X so it will look like this (3x   )(1x    ) now lets find the signs, they are both negative this means that inside the parenthesis there will be 1 with a negative and the other witha positive lets now check the last term. 4 can be either multiplied by 1 and 4 or 2 by 2 so lets see what will fit here. we know that the middle term has to be -4 so if set if you multiply 3 times 4 you will get 12 and minus 1 it wil gibve you 11 so you cant use 1 and 4 so now lets try 2 and 2 plug them in 

(3x  2)(1x  2)  note that I didnt put the signs yet lets first find the numbers to check were to put the sign. when you multiply this it will look like this

3x2  6x  2x  4 now we need to ad common numbers teh only common numbers her are 6x and 2x these are the middle terms so if I need a middle term of -4x which one should be positive and which one will haev to be negative? obviouly 6x has to be negative and 2x positve now your factors will look like this (3x+2)(1x-2) 

How did I know which 2 had the negative well 2 time 1 gives you 2 and 3 times 2 gives you 6 so which one has the -???
 
Now that you haev the factors you have to solve for x in both lets start with the first one 3x+2=0 subtract the 2 to get 3x=-2 now divide your first value of x will be x=-2/3 now lets check the next one 1x-2=0 add the 2 to both sides to get 1x=2 now divide by 1 to get your second x value x=2

so now we know the factors are (3x+2) and (1x-2) and our x values are x=-2/3 and x=2

hope this helped

Answer 2

Answer:

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

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

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

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

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

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