SOLUTION: 5x^2+6x+7=0

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Question 874616: 5x^2+6x+7=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 5%2Ax%5E2%2B6%2Ax%2B7=0 ( notice a=5, b=6, and c=7)





x+=+%28-6+%2B-+sqrt%28+%286%29%5E2-4%2A5%2A7+%29%29%2F%282%2A5%29 Plug in a=5, b=6, and c=7




x+=+%28-6+%2B-+sqrt%28+36-4%2A5%2A7+%29%29%2F%282%2A5%29 Square 6 to get 36




x+=+%28-6+%2B-+sqrt%28+36%2B-140+%29%29%2F%282%2A5%29 Multiply -4%2A7%2A5 to get -140




x+=+%28-6+%2B-+sqrt%28+-104+%29%29%2F%282%2A5%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-6+%2B-+2%2Ai%2Asqrt%2826%29%29%2F%282%2A5%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%28-6+%2B-+2%2Ai%2Asqrt%2826%29%29%2F%2810%29 Multiply 2 and 5 to get 10




After simplifying, the quadratic has roots of


x=-3%2F5%2Bsqrt%2826%29%2F5%2Ai or x=-3%2F5-sqrt%2826%29%2F5%2Ai