Find roots of polynomial $$ p(x) = \frac{135}{2}-95x+\frac{55}{2} $$

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

$$ \begin{aligned}x &= 1 \end{aligned} $$

Step 1:

Get rid of fractions by multipling equation by $ \color{blue}{ 2 } $.

$$ \begin{aligned} \frac{135}{2}-95x+\frac{55}{2} & = 0 ~~~ / \cdot \color{blue}{ 2 } \\[1 em] 135-190x+55 & = 0 \end{aligned} $$

Step 2:

Combine like terms:

$$ \color{blue}{135} -190x+ \color{blue}{55} = -190x+ \color{blue}{190} $$

Step 3:

$$ \begin{aligned} -190x+190 & = 0 \\[1 em] -190 \cdot x & = -190 \\[1 em] x & = - \frac{ 190 }{ -190 } \\[1 em] x & = - \frac{ 190 : 190 }{ -190 : 190} \\[1 em] x & = 1 \end{aligned} $$

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