SOLUTION: Solve the cubic equation: x^3+5832=0

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Question 211449: Solve the cubic equation: x^3+5832=0
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve:
x%5E3%2B5832 This is the sum of two cubes and this is factorable thus:
A%5E3%2BB%5E3+=+%28A%2BB%29%28A%5E2-AB%2BB%5E2%29 So, for this problem:
%28x%29%5E3%2B%2818%29%5E3+=+0
%28x%2B18%29%28x%5E2-18x%2B324%29+=+0
x%2B18+=+0 or x%5E2-18x%2B324+=+0
x+=+-18 or...
x%5E2-18x%2B324+=+0 Use the quadratic formula to solve:x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a where: a = 1, b = -18, and c = 324.
x+=+%28-%28-18%29%2B-sqrt%28%28-18%29%5E2-4%281%29%28324%29%29%29%2F2%281%29 Evaluate:
x+=+%2818%2B-sqrt%28-972%29%29%2F2
x+=+%2818%2B9%2Asqrt%2812%29%29%2F2 or %2818-9%2Asqrt%2812%29%29%2F2
The three solutions are:
x+=+-18
x+=+%2818%2B9%2Asqrt%2812%29%29%2F2
x+=+%2818-9%2Asqrt%2812%29%29%2F2