SOLUTION: Can you determine the complex number solution to this equation. x^2-2x+10=0

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Question 107956: Can you determine the complex number solution to this equation. x^2-2x+10=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve x%5E2-2%2Ax%2B10=0 ( notice a=1, b=-2, and c=10)





x+=+%28--2+%2B-+sqrt%28+%28-2%29%5E2-4%2A1%2A10+%29%29%2F%282%2A1%29 Plug in a=1, b=-2, and c=10




x+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%2A1%2A10+%29%29%2F%282%2A1%29 Negate -2 to get 2




x+=+%282+%2B-+sqrt%28+4-4%2A1%2A10+%29%29%2F%282%2A1%29 Square -2 to get 4 (note: remember when you square -2, you must square the negative as well. This is because %28-2%29%5E2=-2%2A-2=4.)




x+=+%282+%2B-+sqrt%28+4%2B-40+%29%29%2F%282%2A1%29 Multiply -4%2A10%2A1 to get -40




x+=+%282+%2B-+sqrt%28+-36+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%282+%2B-+6%2Ai%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%282+%2B-+6%2Ai%29%2F%282%29 Multiply 2 and 1 to get 2




After simplifying, the quadratic has roots of


x=1%2B3%2Ai or x=1-3%2Ai






So we can see that there are two complex solutions