Question 4359: 5x^3-36x^2+189=0
solve for x
please show work
Answer by khwang(438)   (Show Source):
You can put this solution on YOUR website! Step I) Try to factor out (x-3)
5x^3-36x^2+189=0
i) Separate -36x^2 into two terms:
5x^3- 15x^2 - 21x^2 + 189=0 ,
ii)Regrouping :
5x^2(x -3) - 21(x^2 - 9) = 0
iii) Note (x^2 -9) = (x-3)(x+3) [a formula you should know.]
5x^2(x -3) - 21(x-3)(x+3) = 0
iv) Factor out (x-3):
(x-3)[5x^2 -21(x+3)] = 0,
Or (x-3)[5x^2 -21 x -63] = 0.
Step II:
x - 3 = 0 implies x = 3
By quadratic formula on 5x^2 -21 x -63 = 0
we have x = [21 + sqrt(21^2 + 20 * 63)]/10
= [21 + 9 sqrt(21)]/ 10 (or 3/10[ 7 + 3 sqrt(21)])
or x = [21 - 9 sqrt(21)]/ 10
Kenny
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