Question

Solve -3x^2 - 4x - 4 = 0 using the quadratic formula.

Answer 1

Do you know the quadratic formula?

Answer 2

If you do, how far did you get?

Answer 3

would a be 3 and b be 4 and c be 4?

Answer 4

you multiplied everything by -1 right?

Answer 5

if so, then yes, a = 3, b = 4 and c = 4

Answer 6

okay now i'm stuck at 4 \[4\pm√64 divide everything by -6\]

Answer 7

\[\Large x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\]


\[\Large x = \frac{-(4)\pm\sqrt{(4)^2-4(3)(4)}}{2(3)}\]


\[\Large x = \frac{-4\pm\sqrt{16-(48)}}{6}\]


\[\Large x = \frac{-4\pm\sqrt{-32}}{6}\]


\[\Large x = \frac{-4+\sqrt{-32}}{6} \ \text{or} \ x = \frac{-4-\sqrt{-32}}{6}\]


Making sense so far?

Answer 8

yes

Answer 9

what's next?

Answer 10

since the radicand is negative u have make it a positive so they will be i√32

Answer 11

you can simplify \(\Large \sqrt{32}\) also

Answer 12

and then divide both terms by 6?

Answer 13

\[\Large \sqrt{32} = \sqrt{16*2}\]


\[\Large \sqrt{32} = \sqrt{16}*\sqrt{2}\]


\[\Large \sqrt{32} = 4\sqrt{2}\]

Answer 14

so our updated steps become

\[\Large x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\]


\[\Large x = \frac{-(4)\pm\sqrt{(4)^2-4(3)(4)}}{2(3)}\]


\[\Large x = \frac{-4\pm\sqrt{16-(48)}}{6}\]


\[\Large x = \frac{-4\pm\sqrt{-32}}{6}\]


\[\Large x = \frac{-4+\sqrt{-32}}{6} \ \text{or} \ x = \frac{-4-\sqrt{-32}}{6}\]


\[\Large x = \frac{-4+4i\sqrt{2}}{6} \ \text{or} \ x = \frac{-4-4i\sqrt{2}}{6}\]

Answer 15

will it be \[-2 \pm 4i√2 divided all by 3?\]

Answer 16

you need to divide everything (except for the stuff in the square root) by 2, so

\[\Large x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\]


\[\Large x = \frac{-(4)\pm\sqrt{(4)^2-4(3)(4)}}{2(3)}\]


\[\Large x = \frac{-4\pm\sqrt{16-(48)}}{6}\]


\[\Large x = \frac{-4\pm\sqrt{-32}}{6}\]


\[\Large x = \frac{-4+\sqrt{-32}}{6} \ \text{or} \ x = \frac{-4-\sqrt{-32}}{6}\]


\[\Large x = \frac{-4+4i\sqrt{2}}{6} \ \text{or} \ x = \frac{-4-4i\sqrt{2}}{6}\]


\[\Large x = \frac{-2+2i\sqrt{2}}{3} \ \text{or} \ x = \frac{-2-2i\sqrt{2}}{3}\]

Answer 17

Now you're done. Those are the exact solutions. The approximate solutions can be found with a calculator (find the real and imaginary parts separately)

Answer 18

ohhhhh ok

Answer 19

thanks

Answer 20

np