Answer:
[tex]x1=\frac{-2(+)2i\sqrt{2}} {3}[/tex]
[tex]x2=\frac{-2(-)2i\sqrt{2}} {3}[/tex]
Step-by-step explanation:
we have
[tex]-3x^{2} -4x-4=0[/tex]
Rewrite (Multiply by [tex]-1[/tex] both sides)
[tex]3x^{2}+4x+4=0[/tex]
The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]3x^{2}+4x+4=0[/tex]
so
[tex]a=3\\b=4\\c=4[/tex]
substitute
[tex]x=\frac{-4(+/-)\sqrt{4^{2}-4(3)(4)}} {2(3)}[/tex]
[tex]x=\frac{-4(+/-)\sqrt{-32}} {6}[/tex]
remember that
[tex]i=\sqrt{-1}[/tex]
[tex]x=\frac{-4(+/-)4i\sqrt{2}} {6}[/tex]
Simplify
[tex]x=\frac{-2(+/-)2i\sqrt{2}} {3}[/tex]
[tex]x1=\frac{-2(+)2i\sqrt{2}} {3}[/tex]
[tex]x2=\frac{-2(-)2i\sqrt{2}} {3}[/tex]
