SOLUTION: x^2-8x+27=0 (2x^3)^3 / 5 x 18x^-2 / 2x^3

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Question 549152: x^2-8x+27=0

(2x^3)^3 / 5 x 18x^-2 / 2x^3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first one to get you started.

# 1




x%5E2-8x%2B27=0 Start with the given equation.


Notice that the quadratic x%5E2-8x%2B27 is in the form of Ax%5E2%2BBx%2BC where A=1, B=-8, 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-%28-8%29+%2B-+sqrt%28+%28-8%29%5E2-4%281%29%2827%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-8, and C=27


x+=+%288+%2B-+sqrt%28+%28-8%29%5E2-4%281%29%2827%29+%29%29%2F%282%281%29%29 Negate -8 to get 8.


x+=+%288+%2B-+sqrt%28+64-4%281%29%2827%29+%29%29%2F%282%281%29%29 Square -8 to get 64.


x+=+%288+%2B-+sqrt%28+64-108+%29%29%2F%282%281%29%29 Multiply 4%281%29%2827%29 to get 108


x+=+%288+%2B-+sqrt%28+-44+%29%29%2F%282%281%29%29 Subtract 108 from 64 to get -44


x+=+%288+%2B-+sqrt%28+-44+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%288+%2B-+2i%2Asqrt%2811%29%29%2F%282%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%288%29%2F%282%29+%2B-+%282i%2Asqrt%2811%29%29%2F%282%29 Break up the fraction.


x+=+4+%2B-+sqrt%2811%29%2Ai Reduce.


x+=+4%2Bsqrt%2811%29%2Ai or x+=+4-sqrt%2811%29%2Ai Break up the expression.


So the solutions are x+=+4%2Bsqrt%2811%29%2Ai or x+=+4-sqrt%2811%29%2Ai