Find roots of polynomial $$ p(x) = 3500x+\frac{500}{2}+\frac{800}{4}-5012 $$

The root of polynomial $ p(x) $ is:

$$ \begin{aligned}x &= \frac{ 2281 }{ 1750 } \end{aligned} $$

Step 1:

Get rid of fractions by multipling equation by $ \color{blue}{ 4 } $.

$$ \begin{aligned} 3500x+\frac{500}{2}+\frac{800}{4}-5012 & = 0 ~~~ / \cdot \color{blue}{ 4 } \\[1 em] 14000x+1000+800-20048 & = 0 \end{aligned} $$

Step 2:

Combine like terms:

$$ 14000x+ \color{blue}{1000} + \color{red}{800} \color{red}{-20048} = 14000x \color{red}{-18248} $$

Step 3:

$$ \begin{aligned} 14000x-18248 & = 0 \\[1 em] 14000 \cdot x & = 18248 \\[1 em] x & = \frac{ 18248 }{ 14000 } \\[1 em] x & = \frac{ 18248 : 8 }{ 14000 : 8} \\[1 em] x & = \frac{ 2281 }{ 1750 } \end{aligned} $$

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