Réitigh 0=(x-t)*(e^0.2x-1)

$$0 = ( x - t ) \cdot ( e ^ { 0.2 x } - 1 )$$

Réitigh do t. (complex solution)

$$\left\{\begin{matrix}\\t=x\text{, }&\text{unconditionally}\\t\in \mathrm{C}\text{, }&\exists n_{1}\in \mathrm{Z}\text{ : }x=10\pi n_{1}i\end{matrix}\right.$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

Úsáid an t-airí dáileach chun x-t a mhéadú faoi e^{0.2x}-1.

$$0=xe^{0.2x}-x-te^{0.2x}+t$$

Athraigh na taobhanna ionas go mbeidh na téarmaí inathraitheacha ar fad ar an taobh clé.

$$xe^{0.2x}-x-te^{0.2x}+t=0$$

Bain xe^{0.2x} ón dá thaobh. Is ionann rud ar bith a dhealaítear ó nialas agus a shéanadh.

$$-x-te^{0.2x}+t=-xe^{0.2x}$$

Cuir x leis an dá thaobh.

$$-te^{0.2x}+t=-xe^{0.2x}+x$$

Comhcheangail na téarmaí ar fad ina bhfuil t.

$$\left(-e^{0.2x}+1\right)t=-xe^{0.2x}+x$$

Tá an chothromóid i bhfoirm chaighdeánach.

$$\left(1-e^{\frac{x}{5}}\right)t=x-xe^{\frac{x}{5}}$$

Roinn an dá thaobh faoi -e^{0.2x}+1.

$$\frac{\left(1-e^{\frac{x}{5}}\right)t}{1-e^{\frac{x}{5}}}=\frac{x-xe^{\frac{x}{5}}}{1-e^{\frac{x}{5}}}$$

Má roinntear é faoi -e^{0.2x}+1 cuirtear an iolrúchán faoi -e^{0.2x}+1 ar ceal.

$$t=\frac{x-xe^{\frac{x}{5}}}{1-e^{\frac{x}{5}}}$$

Roinn -xe^{\frac{x}{5}}+x faoi -e^{0.2x}+1.

$$t=x$$

Réitigh do t.

$$\left\{\begin{matrix}\\t=x\text{, }&\text{unconditionally}\\t\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

Úsáid an t-airí dáileach chun x-t a mhéadú faoi e^{0.2x}-1.

$$0=xe^{0.2x}-x-te^{0.2x}+t$$

Athraigh na taobhanna ionas go mbeidh na téarmaí inathraitheacha ar fad ar an taobh clé.

$$xe^{0.2x}-x-te^{0.2x}+t=0$$

Bain xe^{0.2x} ón dá thaobh. Is ionann rud ar bith a dhealaítear ó nialas agus a shéanadh.

$$-x-te^{0.2x}+t=-xe^{0.2x}$$

Cuir x leis an dá thaobh.

$$-te^{0.2x}+t=-xe^{0.2x}+x$$

Comhcheangail na téarmaí ar fad ina bhfuil t.

$$\left(-e^{0.2x}+1\right)t=-xe^{0.2x}+x$$

Tá an chothromóid i bhfoirm chaighdeánach.

$$\left(1-e^{\frac{x}{5}}\right)t=x-xe^{\frac{x}{5}}$$

Roinn an dá thaobh faoi -e^{0.2x}+1.

$$\frac{\left(1-e^{\frac{x}{5}}\right)t}{1-e^{\frac{x}{5}}}=\frac{x-xe^{\frac{x}{5}}}{1-e^{\frac{x}{5}}}$$

Má roinntear é faoi -e^{0.2x}+1 cuirtear an iolrúchán faoi -e^{0.2x}+1 ar ceal.

$$t=\frac{x-xe^{\frac{x}{5}}}{1-e^{\frac{x}{5}}}$$

Roinn -xe^{\frac{x}{5}}+x faoi -e^{0.2x}+1.

$$t=x$$

Réitigh do x. (complex solution)

$$x=t$$

$$x=i\times 10\pi n_{1}\text{, }n_{1}\in \mathrm{Z}$$

Réitigh do x.

$$x=0$$

$$x=t$$