SOLUTION: Solve the polynomial equation 125x^3+216=0 Please show steps thank you

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Question 707869: Solve the polynomial equation 125x^3+216=0
Please show steps thank you
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
125x^3+216 = 0

(5x)^3 + 6^3 = 0

(5x + 6)((5x)^2 - 5x*6 + 6^2) = 0 ... use the sum of cubes formula

(5x + 6)(25x^2 - 30x + 36) = 0

5x + 6 = 0 or 25x^2 - 30x + 36 = 0

5x = -6 or 25x^2 - 30x + 36 = 0

x = -6/5 or 25x^2 - 30x + 36 = 0

So one solution is x = -6/5

The other two solutions can be found by solving 25x^2 - 30x + 36 = 0

You solve 25x^2 - 30x + 36 = 0 for x by using the quadratic formula.