Question

solve 0 = 3x^2 + 18x + 22 using quadratic formula

Answer 1

a = 3
b=18
c=22
\[x = \frac{-b \pm \sqrt{b^{2}-4ac}}{2a}\]

Answer 2

I get down to where I have to get the square root of 60 but 60 isn't a perfect square

Answer 3

Are there any perfect squares as factors of 60?

Answer 4

4*15

Answer 5

\[-18+/- \sqrt{60}\]

Answer 6

Yeah, so we can rewrite it as the sqrt(4*15), and then break it apart
\[ \begin{split}
\sqrt{4*15} &= \sqrt{4} \sqrt{15}\\
&= 2\sqrt{15}\\
\end{split}
\]

Answer 7

so to go along with the equation i posted above, the 2 would be added to the -18?

Answer 8

nope, since the radical is still there, we cannot add them together.
However, since the denominator is 6 (divisible by 2) and the numerator's terms (18 and 2sqrt(15)) are divisible by 2, we can cancel a 2 in both the numerator and the denominator.

\[ \frac{18 \pm 2\sqrt{15}}{6} = \frac{\cancel{2}(9 \pm \sqrt{15})}{\cancel2*3} \]

Answer 9

and since we're not asked to approximate or anything ,its sufficient to leave it as that.

\[ x= \frac{9 \pm \sqrt{15}}{3} \]

Answer 10

what do you write to show the 2's being crossed out ?

Answer 11

oops, I should include the negative. my bad!

Answer 12

what if i was asked ti find the roots? would that answer till be okay?

Answer 13

*to

Answer 14

dumbcow, \cancel{#}
i had to look it up to find out how not long ago. :P

yes, since the roots are the x values that make the equation = 0.

Answer 15

okay, thanks a lot

Answer 16

@dumbcow
\[ \frac{18 \pm 2\sqrt{15}}{6} = \frac{\cancel{2}(9 \pm \sqrt{15})}{\cancel{2}*3} \]
\frac{18 \pm 2\sqrt{15}}{6} = \frac{\cancel{2}(9 \pm \sqrt{15})}{\cancel{2}*3}

\cancel{#}

Answer 17

thanks