SOLUTION: Please help w/ the following: 27x^3-8=0 Thank you.

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Question 59095: Please help w/ the following:
27x^3-8=0
Thank you.
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
Formula for the factoring of the difference of cubes:highlight%28u%5E3-v%5E3=%28u-v%29%28u%5E2%2Buv%2Bv%5E2%29%29
27x%5E3-8=0
%283x%29%5E3-%282%29%5E3=0 u=3x and v=2
%283x-2%29%28%283x%29%5E2%2B%283x%29%282%29%2B%282%29%5E2%29=0
%283x-2%29%289x%5E2%2B6x%2B4%29=0
3x-2=0 and 9x%5E2%2B6x%2B4=0
3x-2%2B2=0%2B2
3x=2
3x%2F3=2%2F3
highlight%28x=2%2F3%29 This is the real solution that we found before. You have to use the quadratic formula to find the complex solution.
When a quadratic equation is in standard form:highlight%280=ax%5E2%2Bbx%2Bc%29 the quadratic formula can be applied: highlight%28x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29%29
For 9x%5E2%2B6x%2B4=0 a=9, b=6 and c=4
x=%28-%286%29%2B-sqrt%28%286%29%5E2-4%289%29%284%29%29%29%2F%282%289%29%29
x=%28-6%2B-sqrt%2836-144%29%29%2F18
x=%28-6%2B-sqrt%28-108%29%29%2F18
x=%28-6%2B-sqrt%28-1%29%2Asqrt%2836%29%2Asqrt%283%29%29%2F18
x=%28-6%2Bor-6%2Asqrt%283%29%2Ai%29%2F18
x=6%28-1%2B-sqrt%283%29%2Ai%29%2F%286%2A3%29
x=%28-1%2B-sqrt%283%29%2Ai%29%2F3
Happy Calculating!!!

Happy Calculating!!!