SOLUTION: Find all solutions of the equation x^2+1x+7=0 and express them in the form a+bi

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Question 843273: Find all solutions of the equation x^2+1x+7=0 and express them in the form a+bi
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%2Bx%2B7=0 ( notice a=1, b=1, and c=7)





x+=+%28-1+%2B-+sqrt%28+%281%29%5E2-4%2A1%2A7+%29%29%2F%282%2A1%29 Plug in a=1, b=1, and c=7




x+=+%28-1+%2B-+sqrt%28+1-4%2A1%2A7+%29%29%2F%282%2A1%29 Square 1 to get 1




x+=+%28-1+%2B-+sqrt%28+1%2B-28+%29%29%2F%282%2A1%29 Multiply -4%2A7%2A1 to get -28




x+=+%28-1+%2B-+sqrt%28+-27+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-1+%2B-+3%2Ai%2Asqrt%283%29%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%28-1+%2B-+3%2Ai%2Asqrt%283%29%29%2F%282%29 Multiply 2 and 1 to get 2




After simplifying, the quadratic has roots of


x=-1%2F2%2B3%2Asqrt%283%29%2F2%2Ai or x=-1%2F2-3%2Asqrt%283%29%2F2%2Ai





note: those solutions are of the form a%2Bbi. In the first case, a+=+-1%2F2, b+=+3%2Asqrt%283%29%2F2
In the second case, a+=+-1%2F2, b+=+-3%2Asqrt%283%29%2F2