SOLUTION: What are the solutions of 3x2 + 6x + 6 = 0?

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Question 470961: What are the solutions of 3x2 + 6x + 6 = 0?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

3x%5E2+%2B+6x+%2B+6+=+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 3%2Ax%5E2%2B6%2Ax%2B6=0 ( notice a=3, b=6, and c=6)





x+=+%28-6+%2B-+sqrt%28+%286%29%5E2-4%2A3%2A6+%29%29%2F%282%2A3%29 Plug in a=3, b=6, and c=6




x+=+%28-6+%2B-+sqrt%28+36-4%2A3%2A6+%29%29%2F%282%2A3%29 Square 6 to get 36




x+=+%28-6+%2B-+sqrt%28+36%2B-72+%29%29%2F%282%2A3%29 Multiply -4%2A6%2A3 to get -72




x+=+%28-6+%2B-+sqrt%28+-36+%29%29%2F%282%2A3%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-6+%2B-+6%2Ai%29%2F%282%2A3%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%28-6+%2B-+6%2Ai%29%2F%286%29 Multiply 2 and 3 to get 6




After simplifying, the quadratic has roots of


x=-1%2Bi or x=-1-i