Whakaoti i te z^2+(x+2)z+y(1-2)=0

$${ z }^{ 2 } +(x+2)z+y(1-2)=0$$

Whakaoti mō x (complex solution)

$$\left\{\begin{matrix}x=-z+\frac{y}{z}-2\text{, }&z\neq 0\\x\in \mathrm{C}\text{, }&y=0\text{ and }z=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te x+2 ki te z.

$$z^{2}+xz+2z+y\left(1-2\right)=0$$

Tangohia te 2 i te 1, ka -1.

$$z^{2}+xz+2z+y\left(-1\right)=0$$

Tangohia te z^{2} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$xz+2z+y\left(-1\right)=-z^{2}$$

Tangohia te 2z mai i ngā taha e rua.

$$xz+y\left(-1\right)=-z^{2}-2z$$

Tangohia te y\left(-1\right) mai i ngā taha e rua.

$$xz=-z^{2}-2z-y\left(-1\right)$$

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

$$xz=-z^{2}-2z+y$$

He hanga arowhānui tō te whārite.

$$zx=y-z^{2}-2z$$

Whakawehea ngā taha e rua ki te z.

$$\frac{zx}{z}=\frac{y-z^{2}-2z}{z}$$

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

$$x=\frac{y-z^{2}-2z}{z}$$

Whakawehe -z^{2}-2z+y ki te z.

$$x=-z+\frac{y}{z}-2$$

Whakaoti mō x

$$\left\{\begin{matrix}x=-z+\frac{y}{z}-2\text{, }&z\neq 0\\x\in \mathrm{R}\text{, }&y=0\text{ and }z=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te x+2 ki te z.

$$z^{2}+xz+2z+y\left(1-2\right)=0$$

Tangohia te 2 i te 1, ka -1.

$$z^{2}+xz+2z+y\left(-1\right)=0$$

Tangohia te z^{2} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$xz+2z+y\left(-1\right)=-z^{2}$$

Tangohia te 2z mai i ngā taha e rua.

$$xz+y\left(-1\right)=-z^{2}-2z$$

Tangohia te y\left(-1\right) mai i ngā taha e rua.

$$xz=-z^{2}-2z-y\left(-1\right)$$

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

$$xz=-z^{2}-2z+y$$

He hanga arowhānui tō te whārite.

$$zx=y-z^{2}-2z$$

Whakawehea ngā taha e rua ki te z.

$$\frac{zx}{z}=\frac{y-z^{2}-2z}{z}$$

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

$$x=\frac{y-z^{2}-2z}{z}$$

Whakawehe -z^{2}-2z+y ki te z.

$$x=-z+\frac{y}{z}-2$$

Whakaoti mō y

$$y=z\left(x+z+2\right)$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te x+2 ki te z.

$$z^{2}+xz+2z+y\left(1-2\right)=0$$

Tangohia te 2 i te 1, ka -1.

$$z^{2}+xz+2z+y\left(-1\right)=0$$

Tangohia te z^{2} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$xz+2z+y\left(-1\right)=-z^{2}$$

Tangohia te xz mai i ngā taha e rua.

$$2z+y\left(-1\right)=-z^{2}-xz$$

Tangohia te 2z mai i ngā taha e rua.

$$y\left(-1\right)=-z^{2}-xz-2z$$

He hanga arowhānui tō te whārite.

$$-y=-xz-z^{2}-2z$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-y}{-1}=-\frac{z\left(x+z+2\right)}{-1}$$

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

$$y=-\frac{z\left(x+z+2\right)}{-1}$$

Whakawehe -z\left(2+z+x\right) ki te -1.

$$y=z\left(x+z+2\right)$$