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

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

Atrast d (complex solution)

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

Lineāra vienādojuma risināšanas darbības

Izmantojiet distributīvo īpašību, lai reizinātu 2x-2 ar d.

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

Izmantojiet distributīvo īpašību, lai reizinātu 2xd-2d ar x.

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

Izmantojiet distributīvo īpašību, lai reizinātu 3y+7 ar y.

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

Atņemiet 3y^{2} no abām pusēm. Atņemot nu nulles jebko, iegūst tā noliegumu.

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

Atņemiet 7y no abām pusēm.

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

Savelciet visus locekļus, kuros ir d.

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

Daliet abas puses ar 2x^{2}-2x.

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

Dalīšana ar 2x^{2}-2x atsauc reizināšanu ar 2x^{2}-2x.

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

Daliet -y\left(7+3y\right) ar 2x^{2}-2x.

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

Atrast d

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

Lineāra vienādojuma risināšanas darbības

Izmantojiet distributīvo īpašību, lai reizinātu 2x-2 ar d.

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

Izmantojiet distributīvo īpašību, lai reizinātu 2xd-2d ar x.

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

Izmantojiet distributīvo īpašību, lai reizinātu 3y+7 ar y.

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

Atņemiet 3y^{2} no abām pusēm. Atņemot nu nulles jebko, iegūst tā noliegumu.

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

Atņemiet 7y no abām pusēm.

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

Savelciet visus locekļus, kuros ir d.

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

Daliet abas puses ar 2x^{2}-2x.

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

Dalīšana ar 2x^{2}-2x atsauc reizināšanu ar 2x^{2}-2x.

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

Daliet -y\left(7+3y\right) ar 2x^{2}-2x.

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

Atrast x (complex solution)

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

Atrast x

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