Question Number 40212 by KMA last updated on 17/Jul/18
$${Solve}\:\mathrm{4}{x}^{\mathrm{2}} −\mathrm{8}{x}−\mathrm{3}=\mathrm{0} \\ $$
Commented by MJS last updated on 17/Jul/18
$${ax}^{\mathrm{2}} +{bx}+{c}=\mathrm{0} \\ $$$${x}=−\frac{{b}}{\mathrm{2}{a}}\pm\frac{\sqrt{{b}^{\mathrm{2}} −\mathrm{4}{ac}}}{\mathrm{2}{a}} \\ $$$$ \\ $$$${x}^{\mathrm{2}} +{px}+{q}=\mathrm{0} \\ $$$${x}=−\frac{{p}}{\mathrm{2}}\pm\frac{\sqrt{{p}^{\mathrm{2}} −\mathrm{4}{q}}}{\mathrm{2}} \\ $$
Answered by tanmay.chaudhury50@gmail.com last updated on 17/Jul/18
$$\left(\mathrm{2}{x}\right)^{\mathrm{2}} −\mathrm{2}.\mathrm{2}{x}.\mathrm{2}+\mathrm{4}−\mathrm{7}=\mathrm{0} \\ $$$$\left(\mathrm{2}{x}−\mathrm{2}\right)^{\mathrm{2}} =\mathrm{7} \\ $$$$\mathrm{2}{x}=\mathrm{2}\pm\sqrt{\mathrm{7}}\: \\ $$$${x}=\frac{\mathrm{2}\pm\sqrt{\mathrm{7}}}{\mathrm{2}} \\ $$
Answered by Rio Mike last updated on 17/Jul/18
$$\:{a}=\:\mathrm{4}\:,{b}=−\mathrm{8}\:,{c}=−\mathrm{3} \\ $$$${x}\:=\:\frac{−{b}\pm\sqrt{{b}^{\mathrm{2}} −\mathrm{4}{ac}\:}\:}{\mathrm{2}{a}} \\ $$$${x}\:=\:\frac{\mathrm{8}\:\pm\:\sqrt{\mathrm{64}−\mathrm{12}}}{\mathrm{8}} \\ $$$${x}=\:\frac{\mathrm{8}\pm\mathrm{7}.\mathrm{2}}{\mathrm{8}} \\ $$$${x}=\:\frac{\mathrm{8}+\mathrm{7}.\mathrm{2}}{\mathrm{8}}\:{or}\:\frac{\mathrm{8}−\mathrm{7}.\mathrm{2}}{\mathrm{8}} \\ $$$$ \\ $$
Commented by tanmay.chaudhury50@gmail.com last updated on 17/Jul/18
$${check}\:{the}\:{value}\:{of}\:\mathrm{4}{ac}\:\: \\ $$