SOLUTION: please solve: x^2+4x+6=0

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Question 490307: please solve: x^2+4x+6=0
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

+x%5E2%2B4x%2B6=0.....use quadratic formula

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%2B4%2Ax%2B6=0 ( notice a=1, b=4, and c=6)





x+=+%28-4+%2B-+sqrt%28+%284%29%5E2-4%2A1%2A6+%29%29%2F%282%2A1%29 Plug in a=1, b=4, and c=6




x+=+%28-4+%2B-+sqrt%28+16-4%2A1%2A6+%29%29%2F%282%2A1%29 Square 4 to get 16




x+=+%28-4+%2B-+sqrt%28+16%2B-24+%29%29%2F%282%2A1%29 Multiply -4%2A6%2A1 to get -24




x+=+%28-4+%2B-+sqrt%28+-8+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-4+%2B-+2%2Ai%2Asqrt%282%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+=+%28-4+%2B-+2%2Ai%2Asqrt%282%29%29%2F%282%29 Multiply 2 and 1 to get 2




After simplifying, the quadratic has roots of


x=-2%2Bsqrt%282%29i or x=-2-sqrt%282%29i