SOLUTION: find all complex solutions of 2x^2-x+6=0thanks

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Question 766915: find all complex solutions of 2x^2-x+6=0thanks
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

+2x%5E2-x%2B6=0
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 2%2Ax%5E2-x%2B6=0 ( notice a=2, b=-1, and c=6)





x+=+%28--1+%2B-+sqrt%28+%28-1%29%5E2-4%2A2%2A6+%29%29%2F%282%2A2%29 Plug in a=2, b=-1, and c=6




x+=+%281+%2B-+sqrt%28+%28-1%29%5E2-4%2A2%2A6+%29%29%2F%282%2A2%29 Negate -1 to get 1




x+=+%281+%2B-+sqrt%28+1-4%2A2%2A6+%29%29%2F%282%2A2%29 Square -1 to get 1 (note: remember when you square -1, you must square the negative as well. This is because %28-1%29%5E2=-1%2A-1=1.)




x+=+%281+%2B-+sqrt%28+1%2B-48+%29%29%2F%282%2A2%29 Multiply -4%2A6%2A2 to get -48




x+=+%281+%2B-+sqrt%28+-47+%29%29%2F%282%2A2%29 Combine like terms in the radicand (everything under the square root)




x+=+%281+%2B-+i%2Asqrt%2847%29%29%2F%282%2A2%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%281+%2B-+i%2Asqrt%2847%29%29%2F%284%29 Multiply 2 and 2 to get 4




After simplifying, the quadratic has roots of


x=1%2F4%2Bsqrt%2847%29%2F4%2Ai or x=1%2F4-sqrt%2847%29%2F4%2Ai