Whakaoti i te left(2x-2right)dx+(3y+7)y=0

$$\left( 2x-2 \right) dx+(3y+7)y=0$$

Whakaoti mō d (complex solution)

$$\left\{\begin{matrix}d=-\frac{y\left(3y+7\right)}{2x\left(x-1\right)}\text{, }&x\neq 1\text{ and }x\neq 0\\d\in \mathrm{C}\text{, }&\left(y=-\frac{7}{3}\text{ and }x=0\right)\text{ or }\left(y=-\frac{7}{3}\text{ and }x=1\right)\text{ or }\left(y=0\text{ and }x=0\right)\text{ or }\left(y=0\text{ and }x=1\right)\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te 2x-2 ki te d.

$$\left(2xd-2d\right)x+\left(3y+7\right)y=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2xd-2d ki te x.

$$2dx^{2}-2dx+\left(3y+7\right)y=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3y+7 ki te y.

$$2dx^{2}-2dx+3y^{2}+7y=0$$

Tangohia te 3y^{2} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$2dx^{2}-2dx+7y=-3y^{2}$$

Tangohia te 7y mai i ngā taha e rua.

$$2dx^{2}-2dx=-3y^{2}-7y$$

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

$$\left(2x^{2}-2x\right)d=-3y^{2}-7y$$

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

$$\frac{\left(2x^{2}-2x\right)d}{2x^{2}-2x}=-\frac{y\left(3y+7\right)}{2x^{2}-2x}$$

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

$$d=-\frac{y\left(3y+7\right)}{2x^{2}-2x}$$

Whakawehe -y\left(7+3y\right) ki te 2x^{2}-2x.

$$d=-\frac{y\left(3y+7\right)}{2x\left(x-1\right)}$$

Whakaoti mō d

$$\left\{\begin{matrix}d=-\frac{y\left(3y+7\right)}{2x\left(x-1\right)}\text{, }&x\neq 1\text{ and }x\neq 0\\d\in \mathrm{R}\text{, }&\left(y=-\frac{7}{3}\text{ and }x=0\right)\text{ or }\left(y=-\frac{7}{3}\text{ and }x=1\right)\text{ or }\left(y=0\text{ and }x=0\right)\text{ or }\left(y=0\text{ and }x=1\right)\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te 2x-2 ki te d.

$$\left(2xd-2d\right)x+\left(3y+7\right)y=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2xd-2d ki te x.

$$2dx^{2}-2dx+\left(3y+7\right)y=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3y+7 ki te y.

$$2dx^{2}-2dx+3y^{2}+7y=0$$

Tangohia te 3y^{2} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$2dx^{2}-2dx+7y=-3y^{2}$$

Tangohia te 7y mai i ngā taha e rua.

$$2dx^{2}-2dx=-3y^{2}-7y$$

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

$$\left(2x^{2}-2x\right)d=-3y^{2}-7y$$

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

$$\frac{\left(2x^{2}-2x\right)d}{2x^{2}-2x}=-\frac{y\left(3y+7\right)}{2x^{2}-2x}$$

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

$$d=-\frac{y\left(3y+7\right)}{2x^{2}-2x}$$

Whakawehe -y\left(7+3y\right) ki te 2x^{2}-2x.

$$d=-\frac{y\left(3y+7\right)}{2x\left(x-1\right)}$$

Whakaoti mō x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{d\left(d-14y-6y^{2}\right)}+d}{2d}\text{; }x=\frac{-\sqrt{d\left(d-14y-6y^{2}\right)}+d}{2d}\text{, }&d\neq 0\\x\in \mathrm{C}\text{, }&\left(y=-\frac{7}{3}\text{ or }y=0\right)\text{ and }d=0\end{matrix}\right.$$

Whakaoti mō x

$$\left\{\begin{matrix}x=\frac{\sqrt{d\left(d-14y-6y^{2}\right)}+d}{2d}\text{; }x=\frac{-\sqrt{d\left(d-14y-6y^{2}\right)}+d}{2d}\text{, }&\left(y\neq 0\text{ and }y\neq -\frac{7}{3}\text{ and }d=6y^{2}+14y\right)\text{ or }\left(d\leq 6y^{2}+14y\text{ and }d<0\right)\text{ or }\left(d\geq 6y^{2}+14y\text{ and }d>0\right)\\x\in \mathrm{R}\text{, }&\left(y=-\frac{7}{3}\text{ or }y=0\right)\text{ and }d=0\end{matrix}\right.$$