SOLUTION: -9x^2 + 3x - 11 = 0 *

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Question 791362: -9x^2 + 3x - 11 = 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 -9%2Ax%5E2%2B3%2Ax-11=0 ( notice a=-9, b=3, and c=-11)





x+=+%28-3+%2B-+sqrt%28+%283%29%5E2-4%2A-9%2A-11+%29%29%2F%282%2A-9%29 Plug in a=-9, b=3, and c=-11




x+=+%28-3+%2B-+sqrt%28+9-4%2A-9%2A-11+%29%29%2F%282%2A-9%29 Square 3 to get 9




x+=+%28-3+%2B-+sqrt%28+9%2B-396+%29%29%2F%282%2A-9%29 Multiply -4%2A-11%2A-9 to get -396




x+=+%28-3+%2B-+sqrt%28+-387+%29%29%2F%282%2A-9%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-3+%2B-+3%2Ai%2Asqrt%2843%29%29%2F%282%2A-9%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%28-3+%2B-+3%2Ai%2Asqrt%2843%29%29%2F%28-18%29 Multiply 2 and -9 to get -18




After simplifying, the quadratic has roots of


x=1%2F6-sqrt%2843%29%2F6%2Ai or x=1%2F6%2Bsqrt%2843%29%2F6%2Ai