Whakaoti i te 0=(x-t)*(e^0.2x-1)

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

Whakaoti mō t (complex solution)

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

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te x-t ki te e^{0.2x}-1.

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

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

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

Tangohia te xe^{0.2x} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

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

Me tāpiri te x ki ngā taha e rua.

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

Pahekotia ngā kīanga tau katoa e whai ana i te t.

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

He hanga arowhānui tō te whārite.

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

Whakawehea ngā taha e rua ki te -e^{0.2x}+1.

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

Mā te whakawehe ki te -e^{0.2x}+1 ka wetekia te whakareanga ki te -e^{0.2x}+1.

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

Whakawehe -xe^{\frac{x}{5}}+x ki te -e^{0.2x}+1.

$$t=x$$

Whakaoti mō t

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

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te x-t ki te e^{0.2x}-1.

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

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

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

Tangohia te xe^{0.2x} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

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

Me tāpiri te x ki ngā taha e rua.

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

Pahekotia ngā kīanga tau katoa e whai ana i te t.

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

He hanga arowhānui tō te whārite.

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

Whakawehea ngā taha e rua ki te -e^{0.2x}+1.

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

Mā te whakawehe ki te -e^{0.2x}+1 ka wetekia te whakareanga ki te -e^{0.2x}+1.

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

Whakawehe -xe^{\frac{x}{5}}+x ki te -e^{0.2x}+1.

$$t=x$$

Whakaoti mō x (complex solution)

$$x=t$$

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

Whakaoti mō x

$$x=0$$

$$x=t$$