SOLUTION: Solve by using the quadratic formula. 6x^2 + x + 1 = 0

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Question 103580This question is from textbook algebra
: Solve by using the quadratic formula. 6x^2 + x + 1 = 0 This question is from textbook algebra

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 6%2Ax%5E2%2Bx%2B1=0 ( notice a=6, b=1, and c=1)





x+=+%28-1+%2B-+sqrt%28+%281%29%5E2-4%2A6%2A1+%29%29%2F%282%2A6%29 Plug in a=6, b=1, and c=1




x+=+%28-1+%2B-+sqrt%28+1-4%2A6%2A1+%29%29%2F%282%2A6%29 Square 1 to get 1




x+=+%28-1+%2B-+sqrt%28+1%2B-24+%29%29%2F%282%2A6%29 Multiply -4%2A1%2A6 to get -24




x+=+%28-1+%2B-+sqrt%28+-23+%29%29%2F%282%2A6%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-1+%2B-+i%2Asqrt%2823%29%29%2F%282%2A6%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%28-1+%2B-+i%2Asqrt%2823%29%29%2F%2812%29 Multiply 2 and 6 to get 12




After simplifying, the quadratic has roots of


x=-1%2F12%2Bsqrt%2823%29%2F12%2Ai or x=-1%2F12-sqrt%2823%29%2F12%2Ai