anonymous one year ago URGENT HElP Where did I go wrong in my problem?!?!?

1. anonymous

2. UsukiDoll

so we have the quadratic equation $x^2+6x+3$ using the discriminant formula $b^2-4ac$ we have $(6)^2-4(1)(3) =36-12 =24$ which is not a perfect square. I need to grab the latex for the quadratic equation brb

3. anonymous

ok, I'll be here

4. UsukiDoll

${x = \frac{{ - 6 \pm \sqrt {24} }}{{2}}}$

5. UsukiDoll

ok the problem lies in the square root... yes it is 24, but we can simplify that further.

6. UsukiDoll

so we need to find the smallest perfect square number

7. anonymous

Oh I get it, so we can do √6 √4 which simplifies into 2√6 which would go away when divided by 2. right?

8. UsukiDoll

yeah

9. anonymous

Also how do I explain why I chose this method?

10. UsukiDoll

${x = \frac{{ - 6 \pm \sqrt {4 \cdot 6 } }}{{2}}} \rightarrow {x = \frac{{ - 6 \pm 2\sqrt {6} }}{{2}}}$ $x = \frac{-6}{2} \pm \frac{2\sqrt{6}}{2} \rightarrow -3 \pm \sqrt{6}$

11. UsukiDoll

First of all, we can't factor this equation. Using the discriminant formula, we obtain 24 and that's not a perfect square number. Therefore, we have to use the quadratic formula.

12. UsukiDoll

Completing the square is useless because we are given a quadratic equation which is similar to the standard quadratic formula of $ax^2+bx+c$

13. UsukiDoll

I don't think we can do graphing either... our equation doesn't start with y =... that's kind of a generic excuse though.

14. anonymous

Ok thank you SO much