SOLUTION: how can i solve this problem using quadratic formula 12x(squared)+3x+27=0

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Question 315637: how can i solve this problem using quadratic formula
12x(squared)+3x+27=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

12x%5E2%2B3x%2B27=0 Start with the given equation.


Notice that the quadratic 12x%5E2%2B3x%2B27 is in the form of Ax%5E2%2BBx%2BC where A=12, B=3, and C=27


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%283%29+%2B-+sqrt%28+%283%29%5E2-4%2812%29%2827%29+%29%29%2F%282%2812%29%29 Plug in A=12, B=3, and C=27


x+=+%28-3+%2B-+sqrt%28+9-4%2812%29%2827%29+%29%29%2F%282%2812%29%29 Square 3 to get 9.


x+=+%28-3+%2B-+sqrt%28+9-1296+%29%29%2F%282%2812%29%29 Multiply 4%2812%29%2827%29 to get 1296


x+=+%28-3+%2B-+sqrt%28+-1287+%29%29%2F%282%2812%29%29 Subtract 1296 from 9 to get -1287


x+=+%28-3+%2B-+sqrt%28+-1287+%29%29%2F%2824%29 Multiply 2 and 12 to get 24.


x+=+%28-3+%2B-+3i%2Asqrt%28143%29%29%2F%2824%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-3%2B3i%2Asqrt%28143%29%29%2F%2824%29 or x+=+%28-3-3i%2Asqrt%28143%29%29%2F%2824%29 Break up the expression.


x+=+%28-1%2Bi%2Asqrt%28143%29%29%2F%288%29 or x+=+%28-1-i%2Asqrt%28143%29%29%2F%288%29 Reduce.


So the solutions are x+=+%28-1%2Bi%2Asqrt%28143%29%29%2F%288%29 or x+=+%28-1-i%2Asqrt%28143%29%29%2F%288%29