Question Number 192862 by Red1ight last updated on 30/May/23
$$\mathrm{Solve}\:\mathrm{for}\:{x} \\ $$$${x}^{\mathrm{3}} −\mathrm{115}{x}+\mathrm{150}=\mathrm{0} \\ $$
Answered by Frix last updated on 30/May/23
$$\left({x}−\mathrm{10}\right)\left({x}^{\mathrm{2}} +\mathrm{10}{x}−\mathrm{15}\right)=\mathrm{0} \\ $$$${x}_{\mathrm{1}} =\mathrm{10} \\ $$$${x}_{\mathrm{2},\:\mathrm{3}} =−\mathrm{5}\pm\mathrm{2}\sqrt{\mathrm{10}} \\ $$
Commented by Frix last updated on 30/May/23
$$\mathrm{First}\:\mathrm{try}\:\mathrm{all}\:\pm\mathrm{factors}\:\mathrm{of}\:\mathrm{the}\:\mathrm{constant}\:\mathrm{150} \\ $$
Commented by Red1ight last updated on 30/May/23
$$\mathrm{how}\:\mathrm{do}\:\mathrm{you}\:\mathrm{achieve}\:\mathrm{this}\:\mathrm{factorization}? \\ $$
Commented by York12 last updated on 30/May/23
$${intuition} \\ $$