Whakaoti i te ax^2=a+b-bx

$$a x ^ { 2 } = a + b - b x$$

Whakaoti mō a (complex solution)

$$\left\{\begin{matrix}a=-\frac{b}{x+1}\text{, }&x\neq -1\\a\in \mathrm{C}\text{, }&x=1\text{ or }\left(b=0\text{ and }x=-1\right)\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te a mai i ngā taha e rua.

$$ax^{2}-a=b-bx$$

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

$$\left(x^{2}-1\right)a=b-bx$$

Whakawehea ngā taha e rua ki te x^{2}-1.

$$\frac{\left(x^{2}-1\right)a}{x^{2}-1}=\frac{b-bx}{x^{2}-1}$$

Mā te whakawehe ki te x^{2}-1 ka wetekia te whakareanga ki te x^{2}-1.

$$a=\frac{b-bx}{x^{2}-1}$$

Whakawehe b-bx ki te x^{2}-1.

$$a=-\frac{b}{x+1}$$

Whakaoti mō b (complex solution)

$$\left\{\begin{matrix}\\b=-a\left(x+1\right)\text{, }&\text{unconditionally}\\b\in \mathrm{C}\text{, }&x=1\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$a+b-bx=ax^{2}$$

Tangohia te a mai i ngā taha e rua.

$$b-bx=ax^{2}-a$$

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

$$\left(1-x\right)b=ax^{2}-a$$

Whakawehea ngā taha e rua ki te 1-x.

$$\frac{\left(1-x\right)b}{1-x}=\frac{a\left(x^{2}-1\right)}{1-x}$$

Mā te whakawehe ki te 1-x ka wetekia te whakareanga ki te 1-x.

$$b=\frac{a\left(x^{2}-1\right)}{1-x}$$

Whakawehe a\left(x^{2}-1\right) ki te 1-x.

$$b=-a\left(x+1\right)$$

Whakaoti mō a

$$\left\{\begin{matrix}a=-\frac{b}{x+1}\text{, }&x\neq -1\\a\in \mathrm{R}\text{, }&x=1\text{ or }\left(b=0\text{ and }x=-1\right)\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te a mai i ngā taha e rua.

$$ax^{2}-a=b-bx$$

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

$$\left(x^{2}-1\right)a=b-bx$$

Whakawehea ngā taha e rua ki te x^{2}-1.

$$\frac{\left(x^{2}-1\right)a}{x^{2}-1}=\frac{b-bx}{x^{2}-1}$$

Mā te whakawehe ki te x^{2}-1 ka wetekia te whakareanga ki te x^{2}-1.

$$a=\frac{b-bx}{x^{2}-1}$$

Whakawehe b-bx ki te x^{2}-1.

$$a=-\frac{b}{x+1}$$

Whakaoti mō b

$$\left\{\begin{matrix}\\b=-a\left(x+1\right)\text{, }&\text{unconditionally}\\b\in \mathrm{R}\text{, }&x=1\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$a+b-bx=ax^{2}$$

Tangohia te a mai i ngā taha e rua.

$$b-bx=ax^{2}-a$$

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

$$\left(1-x\right)b=ax^{2}-a$$

Whakawehea ngā taha e rua ki te 1-x.

$$\frac{\left(1-x\right)b}{1-x}=\frac{a\left(x^{2}-1\right)}{1-x}$$

Mā te whakawehe ki te 1-x ka wetekia te whakareanga ki te 1-x.

$$b=\frac{a\left(x^{2}-1\right)}{1-x}$$

Whakawehe a\left(x^{2}-1\right) ki te 1-x.

$$b=-a\left(x+1\right)$$