Question
$$25 \cdot \frac{x}{x}-1+\frac{5}{2}x = 2$$
Answer
$$ \begin{matrix}x_1 = 0 & x_2 = -\dfrac{ 44 }{ 5 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 25 \cdot \frac{x}{x}-1+\frac{5}{2}x &= 2&& \text{multiply ALL terms by } \color{blue}{ x\cdot2 }. \\[1 em]x\cdot2\cdot25 \cdot \frac{x}{x}-x\cdot2\cdot1+x\cdot2\frac{5}{2}x &= x\cdot2\cdot2&& \text{cancel out the denominators} \\[1 em]50x-2x+5x^2 &= 4x&& \text{simplify left side} \\[1 em]5x^2+48x &= 4x&& \text{move all terms to the left hand side } \\[1 em]5x^2+48x-4x &= 0&& \text{simplify left side} \\[1 em]5x^2+44x &= 0&& \\[1 em] \end{aligned} $$
In order to solve $ \color{blue}{ 5x^{2}+44x = 0 } $, first we need to factor our $ x $.
$$ 5x^{2}+44x = x \left( 5x+44 \right) $$$ x = 0 $ is a root of multiplicity $ 1 $.
The second root can be found by solving equation $ 5x+44 = 0$.
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