## Math without words (*)

$$x,p,q>0$$
1. $$x^{2}+px=q$$ (Al-Khwarizmi)
2. $$x^{2}+px=q$$ (outra versão) (Al-Khwarizmi)
3. $$x^{2}+q=px(x<\frac{p}{2})$$ (Al-Khwarizmi)
4. $$x^{2}+q=px(x>\frac{p}{2})$$ (Al-Hamid Ibn Turk)
5. $$px+q=x^{2}$$ (Al-Khwarizmi)
Note: The applets only find the positive solutions of the indicated equations, since the unknown $$x$$ is considered as the length of a line segment. The equation $$x^{2}+q=px$$ has only two positive solutions if and only if $$p^{2}>4q$$. The positive solution of the equation $$px+q=x^{2}$$ is always greater than $$p$$.