2x−50​+492x−51​+482x−52​+472x−53​+252x−200​=0

\(\frac{2 x - 50}{50} + \frac{2 x - 51}{49} + \frac{2 x - 52}{48} + \frac{2 x - 53}{47} + \frac{2 x - 100}{25} + \frac{- 100}{25} = 0\)

\(\frac{2 x - 50}{50} + \frac{2 x - 51}{49} + \frac{2 x - 52}{48} + \frac{2 x - 53}{47} + \frac{2 x - 100}{25} + \left(\right. - 4 \left.\right) = 0\)

\(\frac{2 x - 50}{50} - 1 + \frac{2 x - 51}{49} - 1 + \frac{2 x - 52}{48} - 1 + \frac{2 x - 53}{47} - 1 + \frac{2 x - 100}{25} = 0\)

\(\frac{2 x - 100}{50} + \frac{2 x - 100}{49} + \frac{2 x - 100}{48} + \frac{2 x - 100}{47} + \frac{2 x - 100}{25} = 0\)

\(\left(\right. 2 x - 100 \left.\right) . \left(\right. \frac{1}{50} + \frac{1}{49} + \frac{1}{48} + \frac{1}{47} + \frac{1}{25} \left.\right) = 0\)

\(2 x - 100 = 0\) (Do \(\frac{1}{50} + \frac{1}{49} + \frac{1}{48} + \frac{1}{47} + \frac{1}{25} \neq 0\))

\(x = 50\).

Vậy phương trình đã cho có nghiệm \(x = 50\).