SOLUTION: Hi! I'm having some difficulty with the following problem using the quadratic formula and finding the answers to "x." Find all solutions of the equation and express them in the f

Algebra ->  Equations -> SOLUTION: Hi! I'm having some difficulty with the following problem using the quadratic formula and finding the answers to "x." Find all solutions of the equation and express them in the f      Log On


   

Question 196533: Hi!
I'm having some difficulty with the following problem using the quadratic formula and finding the answers to "x."
Find all solutions of the equation and express them in the form a + bi.
x^2+2x+2=0
thanks!
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
x^2+2x+2=0
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The onsite solver does a good job.
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B2x%2B2+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%282%29%5E2-4%2A1%2A2=-4.

The discriminant -4 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -4 is + or - sqrt%28+4%29+=+2.

The solution is x%5B12%5D+=+%28-2%2B-i%2Asqrt%28+-4+%29%29%2F2%5C1+=++%28-2%2B-i%2A2%29%2F2%5C1+, or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B2%2Ax%2B2+%29


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Except for reducing.
It's -1 ± i