This is equation is giving me issues $x^2 - 6x + 15 = 0 $

Question

I was given this equation $x^2 - 6x + 15 = 0 $

I tried to look for numbers whose sum is big and product of ac and i could not find any. I tried using the quadratic formula $$\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$ and this is what i got

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

I just dont know what to do from here: any help would be appreacited.

The equation simply has 2 imaginary roots. – RK01 Jul 17 '15 at 16:00 — RK01, Jul 17 '15 at 16:00
Yes, this equation has no real solutions. – kennytm Jul 17 '15 at 16:00 — kennytm, Jul 17 '15 at 16:00
you must learn more about imaginary numbers – Abr001am Jul 17 '15 at 16:02 — Abr001am, Jul 17 '15 at 16:02
@cardinal $\sqrt{-24} = \sqrt{24} \cdot i$. – James Jul 17 '15 at 16:25 — James, Jul 17 '15 at 16:25

3SAT · Answer 1 · 2015-07-17T16:14:33.610

2

Another approach

$$x^2-6x+15=0$$

$$x^2-6x=-15$$

$$x^2-6x+9=-6$$

$$(x-3)^2=-6$$

Take the square root of both sides

$$x-3=i\sqrt6,\;x-3=-i\sqrt6$$

$$\boxed{\color{red}{x=3\pm i\sqrt6}}$$

edited Jul 17 '15 at 16:14

answered Jul 17 '15 at 16:09

3SAT

7,512

It looks like i didnt fathom this so what would this be? $\sqrt{-47}$ – Jul 17 '15 at 16:52
@user249954 $\sqrt{-47}=i\sqrt{47}$ – 3SAT Jul 18 '15 at 17:47

John_dydx · Accepted Answer · 2015-07-17T16:59:31.637

1

So you need to find the roots as follow: Note that:

$$ i^2 = -1$$

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

$$ x= \frac{6\pm 2i\sqrt{6}}{2} = 3\pm i\sqrt{6}$$

Further explanation ($i^2 = -1$):

let $a = \sqrt{-24}$

$a^2 = -24= 24 \times -1= 24i^2$

$a =\pm \sqrt{24} \times \sqrt{i^2}= \pm i\sqrt{24} = \pm i \times \sqrt{4} \times \sqrt{6} = \pm2i\sqrt{6}$

edited Jul 17 '15 at 16:59

answered Jul 17 '15 at 16:01

John_dydx

4,198

the writing $i=\sqrt{-1}$ is false you must put $i²=-1$ instead – Abr001am Jul 17 '15 at 16:03
@Agawa001, Thanks for your comment. – John_dydx Jul 17 '15 at 16:05
Any reasons for the downvotes? Makes no sense to me! – John_dydx Jul 17 '15 at 16:20
1

I didn't downvoted but it should be $\color{red}+ 6$ – 3SAT Jul 17 '15 at 16:21
now it looks better – 3SAT Jul 17 '15 at 16:22
please can you explain the steps? I will appreciate. like how you got $2i\sqrt{6}$ – Jul 17 '15 at 16:45
@user249954, but you've accepted the above answer and you stated you understood the solution. You may want to read this-http://www.purplemath.com/modules/complex.htm – John_dydx Jul 17 '15 at 16:51
Actually I thought i did until i tried the next one and didnt. Sorry about that, – Jul 17 '15 at 16:53
@user249954, I'll re-edit my post to explain further. – John_dydx Jul 17 '15 at 16:54

This is equation is giving me issues $x^2 - 6x + 15 = 0 $

2 Answers2