[tex]\displaystyle\bf\\\frac{1}{100}x^2-\frac{1}{64}=0\\\\\\\frac{x^2}{100}-\frac{1}{64}=0\\\\\\\frac{x^2}{10^2}-\frac{1}{8^2}=0\\\\\\\left(\frac{x}{10}\right)^{\b2}-\left(\frac{1}{8}\right)^{\b2}=0\\\\[/tex]
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[tex]\displaystyle\bf\\Folosim~formula:~~~a^2-b^2=(a-b)(a+b)\\\\\left(\frac{x}{10}-\frac{1}{8}\right)\left(\frac{x}{10}+\frac{1}{8}\right)=0\\\\\\\frac{x}{10}-\frac{1}{8}=0~\implies~\frac{x}{10}=\frac{1}{8}~\implies~x_1=\frac{10}{8}~\implies~\boxed{\bf~x_1=\frac{5}{4}}\\\\\\\frac{x}{10}+\frac{1}{8}=0~\implies~\frac{x}{10}=-\frac{1}{8}~\implies~x_2=-\frac{10}{8}~\implies~\boxed{\bf~x_2=-\frac{5}{4}}[/tex]
