Whakaoti i te ar_{1}=a(1-e)

$$a r _ { 1 } = a ( 1 - e )$$

Whakaoti mō a (complex solution)

$$\left\{\begin{matrix}\\a=0\text{, }&\text{unconditionally}\\a\in \mathrm{C}\text{, }&r_{1}=1-e\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te a ki te 1-e.

$$ar_{1}=a-ae$$

Tangohia te a mai i ngā taha e rua.

$$ar_{1}-a=-ae$$

Me tāpiri te ae ki ngā taha e rua.

$$ar_{1}-a+ae=0$$

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

$$\left(r_{1}-1+e\right)a=0$$

He hanga arowhānui tō te whārite.

$$\left(r_{1}+e-1\right)a=0$$

Whakawehe 0 ki te r_{1}-1+e.

$$a=0$$

Whakaoti mō r_1 (complex solution)

$$\left\{\begin{matrix}\\r_{1}=1-e\text{, }&\text{unconditionally}\\r_{1}\in \mathrm{C}\text{, }&a=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te a ki te 1-e.

$$ar_{1}=a-ae$$

He hanga arowhānui tō te whārite.

$$ar_{1}=a-ea$$

Whakawehea ngā taha e rua ki te a.

$$\frac{ar_{1}}{a}=\frac{a-ea}{a}$$

Mā te whakawehe ki te a ka wetekia te whakareanga ki te a.

$$r_{1}=\frac{a-ea}{a}$$

Whakawehe a-ae ki te a.

$$r_{1}=1-e$$

Whakaoti mō a

$$\left\{\begin{matrix}\\a=0\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&r_{1}=1-e\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te a ki te 1-e.

$$ar_{1}=a-ae$$

Tangohia te a mai i ngā taha e rua.

$$ar_{1}-a=-ae$$

Me tāpiri te ae ki ngā taha e rua.

$$ar_{1}-a+ae=0$$

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

$$\left(r_{1}-1+e\right)a=0$$

He hanga arowhānui tō te whārite.

$$\left(r_{1}+e-1\right)a=0$$

Whakawehe 0 ki te r_{1}-1+e.

$$a=0$$

Whakaoti mō r_1

$$\left\{\begin{matrix}\\r_{1}=1-e\text{, }&\text{unconditionally}\\r_{1}\in \mathrm{R}\text{, }&a=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te a ki te 1-e.

$$ar_{1}=a-ae$$

He hanga arowhānui tō te whārite.

$$ar_{1}=a-ea$$

Whakawehea ngā taha e rua ki te a.

$$\frac{ar_{1}}{a}=\frac{a-ea}{a}$$

Mā te whakawehe ki te a ka wetekia te whakareanga ki te a.

$$r_{1}=\frac{a-ea}{a}$$

Whakawehe a-ae ki te a.

$$r_{1}=1-e$$