Question

Solve this x²+8/10 -x = 10/2

Answer 1

$x^2+\frac{8}{10}-x=\frac{10}{2}\\ x^2-x+\frac{8}{10}-\frac{10}{2}=0\\ x^2-x+\frac{8}{10}-\frac{50}{10}=0\\ x^2-x-\frac{42}{10}=0\\ x^2-x+\frac{1}{4}-\frac{1}{4}-\frac{42}{10}=0\\ (x-\frac{1}{2})^2=\frac{1}{4}+\frac{42}{10}\\ (x-\frac{1}{2})^2=\frac{5}{20}+\frac{84}{20}\\ (x-\frac{1}{2})^2=\frac{89}{20}\\ x-\frac{1}{2}=\sqrt{\frac{89}{20}} \vee x-\frac{1}{2}=-\sqrt{\frac{89}{20}}\\ x=\frac{1}{2}+\frac{\sqrt{89}}{\sqrt{20}} \vee x=\frac{1}{2}-\frac{\sqrt{89}}{\sqrt{20}}$
$x=\frac{1}{2}+\frac{\sqrt{89}}{2\sqrt{5}} \vee x=\frac{1}{2}-\frac{\sqrt{89}}{2\sqrt5}}\\ x=\frac{1}{2}+\frac{\sqrt{445}}{10} \vee x=\frac{1}{2}-\frac{\sqrt{445}}{10}}\\ x=\frac{5+\sqrt{445}}{10} \vee x=\frac{5-\sqrt{445}}{10}}$