Whakaoti i te A=x^2-2(m-1)x-2m+1

$$A = x ^ { 2 } - 2 ( m - 1 ) x - 2 m + 1$$

Whakaoti mō m (complex solution)

$$\left\{\begin{matrix}m=\frac{x^{2}+2x-A+1}{2\left(x+1\right)}\text{, }&x\neq -1\\m\in \mathrm{C}\text{, }&A=0\text{ and }x=-1\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$x^{2}-2\left(m-1\right)x-2m+1=A$$

Tangohia te 1 mai i ngā taha e rua.

$$x^{2}-2\left(m-1\right)x-2m=A-1$$

Whakamahia te āhuatanga tohatoha hei whakarea te -2 ki te m-1.

$$x^{2}+\left(-2m+2\right)x-2m=A-1$$

Whakamahia te āhuatanga tohatoha hei whakarea te -2m+2 ki te x.

$$x^{2}-2mx+2x-2m=A-1$$

Tangohia te x^{2} mai i ngā taha e rua.

$$-2mx+2x-2m=A-1-x^{2}$$

Tangohia te 2x mai i ngā taha e rua.

$$-2mx-2m=A-1-x^{2}-2x$$

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

$$\left(-2x-2\right)m=A-1-x^{2}-2x$$

He hanga arowhānui tō te whārite.

$$\left(-2x-2\right)m=-x^{2}-2x+A-1$$

Whakawehea ngā taha e rua ki te -2x-2.

$$\frac{\left(-2x-2\right)m}{-2x-2}=\frac{-\left(x+1\right)^{2}+A}{-2x-2}$$

Mā te whakawehe ki te -2x-2 ka wetekia te whakareanga ki te -2x-2.

$$m=\frac{-\left(x+1\right)^{2}+A}{-2x-2}$$

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

$$m=-\frac{-x^{2}-2x+A-1}{2\left(x+1\right)}$$

Whakaoti mō A

$$A=\left(x+1\right)\left(x-2m+1\right)$$

Ngā Upane Otinga

Whakareatia te -1 ki te 2, ka -2.

$$A=x^{2}-2\left(m-1\right)x-2m+1$$

Whakamahia te āhuatanga tohatoha hei whakarea te -2 ki te m-1.

$$A=x^{2}+\left(-2m+2\right)x-2m+1$$

Whakamahia te āhuatanga tohatoha hei whakarea te -2m+2 ki te x.

$$A=x^{2}-2mx+2x-2m+1$$

Whakaoti mō m

$$\left\{\begin{matrix}m=\frac{x^{2}+2x-A+1}{2\left(x+1\right)}\text{, }&x\neq -1\\m\in \mathrm{R}\text{, }&A=0\text{ and }x=-1\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$x^{2}-2\left(m-1\right)x-2m+1=A$$

Tangohia te 1 mai i ngā taha e rua.

$$x^{2}-2\left(m-1\right)x-2m=A-1$$

Whakamahia te āhuatanga tohatoha hei whakarea te -2 ki te m-1.

$$x^{2}+\left(-2m+2\right)x-2m=A-1$$

Whakamahia te āhuatanga tohatoha hei whakarea te -2m+2 ki te x.

$$x^{2}-2mx+2x-2m=A-1$$

Tangohia te x^{2} mai i ngā taha e rua.

$$-2mx+2x-2m=A-1-x^{2}$$

Tangohia te 2x mai i ngā taha e rua.

$$-2mx-2m=A-1-x^{2}-2x$$

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

$$\left(-2x-2\right)m=A-1-x^{2}-2x$$

He hanga arowhānui tō te whārite.

$$\left(-2x-2\right)m=-x^{2}-2x+A-1$$

Whakawehea ngā taha e rua ki te -2x-2.

$$\frac{\left(-2x-2\right)m}{-2x-2}=\frac{-\left(x+1\right)^{2}+A}{-2x-2}$$

Mā te whakawehe ki te -2x-2 ka wetekia te whakareanga ki te -2x-2.

$$m=\frac{-\left(x+1\right)^{2}+A}{-2x-2}$$

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

$$m=-\frac{-x^{2}-2x+A-1}{2\left(x+1\right)}$$