Question
$$\frac{x}{2} = -\frac{1}{8}x^2+2x$$
Answer
$$ \begin{matrix}x_1 = 0 & x_2 = 12 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{x}{2} &= -\frac{1}{8}x^2+2x&& \text{multiply ALL terms by } \color{blue}{ 8 }. \\[1 em]8 \cdot \frac{x}{2} &= -8 \cdot \frac{1}{8}x^2+8\cdot2x&& \text{cancel out the denominators} \\[1 em]4x &= -x^2+16x&& \text{move all terms to the left hand side } \\[1 em]4x+x^2-16x &= 0&& \text{simplify left side} \\[1 em]x^2-12x &= 0&& \\[1 em] \end{aligned} $$
In order to solve $ \color{blue}{ x^{2}-12x = 0 } $, first we need to factor our $ x $.
$$ x^{2}-12x = x \left( x-12 \right) $$$ x = 0 $ is a root of multiplicity $ 1 $.
The second root can be found by solving equation $ x-12 = 0$.
This page was created using
Equations Solver