(Quadratic equations - Completing the square) What is this last step i'm not doing?

[codyw1996]

Okay, so i'm having this same issue with several problems, take the following problem for example. 6x^2+12x+63=0.

The solution that I arrive at is x= -1 (+/-) (i*sqrt(38))/2)
but, the given solution is x=(-2(+/-) i*sqrt(38))/2

I used a few online step by step expression calculators (mathway, cymath, and tiger algebra) and they all confirmed that my solution is correct. So, I asked about this on Yahoo answers and the answerer just put down that the two solutions are equal, but they didn't explain why and I can't find a way to make them equal.
Thanks.

 

[mmm4444bot]

Okay, so i'm having this same issue with several problems, take the following problem for example. 6x^2+12x+63=0.

The solution that I arrive at is x= -1 (+/-) (i*sqrt(38))/2)
but, the given solution is x=(-2(+/-) i*sqrt(38))/2

I used a few online step by step expression calculators (mathway, cymath, and tiger algebra) and they all confirmed that my solution is correct. So, I asked about this on Yahoo answers and the answerer just put down that the two solutions are equal, but they didn't explain why and I can't find a way to make them equal.
Thanks.

Decompose the given solution into a sum and difference of two ratios.

\(\displaystyle \dfrac{-2 \pm i\cdot\sqrt{38}}{2} = \dfrac{-2}{2} \pm \dfrac{i\cdot\sqrt{38}}{2}\)

-2/2 simplifies to -1. :cool:

 

[codyw1996]

Thanks. What I got out of this is that I can just combine the fractions as long as they have a common denominator. I already knew that but I just didn't see it.