Question Number 165243 by Zaynal last updated on 28/Jan/22
$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\lfloor\boldsymbol{\mathrm{Find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{{x}}???\rfloor \\ $$$$\:\:\:\lfloor\mathrm{5}\boldsymbol{{x}}\:+\:\frac{\mathrm{5}\boldsymbol{{x}}}{\left(\mathrm{5}\:+\:\mathrm{5}\right)^{\mathrm{5}} }\:×\:\left(−\mathrm{5}\boldsymbol{{x}}\right)\:\boldsymbol{\div}\:\mathrm{555}\boldsymbol{{x}}\:−\mathrm{55}\boldsymbol{{x}}\:×\frac{\mathrm{5}\boldsymbol{\div}\mathrm{5}}{\mathrm{5}}\:\:+\:\boldsymbol{{x}}\:=\:\mathrm{555555555555555}\rfloor \\ $$$$\:^{\mathrm{proof}:\mathrm{z}.\mathrm{a}} \\ $$
Answered by alephzero last updated on 28/Jan/22
$$\mathrm{5}{x}+\frac{\mathrm{5}{x}}{\left(\mathrm{5}+\mathrm{5}\right)^{\mathrm{5}} }×\left(−\mathrm{5}{x}\right)\boldsymbol{\div}\mathrm{555}{x}−\mathrm{55}{x}× \\ $$$$×\frac{\mathrm{5}/\mathrm{5}}{\mathrm{5}}+{x}=\mathrm{55555555555555} \\ $$$$\mathrm{5}{x}−\frac{\cancel{\mathrm{10}}{x}^{\cancel{\mathrm{2}}} }{\cancel{\mathrm{10}}×\mathrm{10}^{\mathrm{4}} }×\frac{\mathrm{1}}{\mathrm{555}\cancel{{x}}}−\cancel{\mathrm{55}}{x}×\frac{\mathrm{1}}{\cancel{\mathrm{5}}}+{x}= \\ $$$$=\mathrm{5}{x}−\frac{{x}}{\mathrm{10}^{\mathrm{4}} ×\mathrm{555}}−\mathrm{11}{x}+{x}= \\ $$$$=\mathrm{5}{x}−\frac{{x}}{\mathrm{10}^{\mathrm{4}} ×\mathrm{555}}−\mathrm{10}{x}= \\ $$$$=−\mathrm{5}{x}−\frac{{x}}{\mathrm{5550000}}=\mathrm{555555555555555} \\ $$$$−\frac{\mathrm{27750001}{x}}{\mathrm{5550000}}=\mathrm{555555555555555} \\ $$$$\Rightarrow{x}=−\frac{\mathrm{5550000}×\mathrm{555555555555555}}{\mathrm{27750001}} \\ $$