What is 625x-100x^2+4x^3>1000 ?

The solution to 625x-100x^2+4x^3>1000 is 5/2 (45+5sqrt(17))/4

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625x-100x^2+4x^3>1000

625 x - 100 x^{2} + 4 x^{3} > 1000

\frac{5}{2} < x < \frac{45 - 5 17}{4} or x > \frac{45 + 5 17}{4}

Interval Notation

(\frac{5}{2}, \frac{45 - 5 17}{4}) \cup (\frac{45 + 5 17}{4}, \infty)

Decimal Notation

2.5 < x < 6.09611 \dots or x > 16.40388 \dots

Solution steps

625 x - 100 x^{2} + 4 x^{3} > 1000

Rewrite in standard form

625 x - 100 x^{2} + 4 x^{3} - 1000 > 0

Factor

625 x - 100 x^{2} + 4 x^{3} - 1000 : (2 x - 5) (x - \frac{45 + 5 17}{4}) (x - \frac{45 - 5 17}{4})

(2 x - 5) (x - \frac{45 + 5 17}{4}) (x - \frac{45 - 5 17}{4}) > 0

Identify the intervals

\frac{5}{2} < x < \frac{45 - 5 17}{4} or x > \frac{45 + 5 17}{4}

2 a^{2} b - 4 a b^{2}

\frac{1}{3} (2 x + 8) + \frac{4 x - 8}{6} = - x + \frac{7}{2}

\frac{5 ^{2} 5 ^{3}}{5 ^{3} 5 ^{2}}

e^{- \frac{( - 1 )}{\frac{100}{10}}}

\frac{x ( x + 2 )}{5} + 1 = x + \frac{6}{10}

What is 625x-100x^2+4x^3>1000 ?
The solution to 625x-100x^2+4x^3>1000 is 5/2 <x<(45-5sqrt(17))/4 \lor x>(45+5sqrt(17))/4