Atrisiniet x/3*3+x/4*4+x/6*xs+(x/4-8)*2=504

$$\frac { x } { 3 } \times 3 + \frac { x } { 4 } \times 4 + \frac { x } { 6 } \cdot x s + ( \frac { x } { 4 } - 8 ) \cdot 2 = 504$$

Atrast s

$$s=-\frac{15\left(x-208\right)}{x^{2}}$$

$$x\neq 0$$

Lineāra vienādojuma risināšanas darbības

Reiziniet abas vienādojuma puses ar 12, kas ir mazākais 3,4,6 skaitlis, kas dalās bez atlikuma.

$$4x\times 3+3x\times 4+2xxs+12\left(\frac{x}{4}-8\right)\times 2=6048$$

Reiziniet x un x, lai iegūtu x^{2}.

$$4x\times 3+3x\times 4+2x^{2}s+12\left(\frac{x}{4}-8\right)\times 2=6048$$

Reiziniet 4 un 3, lai iegūtu 12.

$$12x+3x\times 4+2x^{2}s+12\left(\frac{x}{4}-8\right)\times 2=6048$$

Reiziniet 3 un 4, lai iegūtu 12.

$$12x+12x+2x^{2}s+12\left(\frac{x}{4}-8\right)\times 2=6048$$

Savelciet 12x un 12x, lai iegūtu 24x.

$$24x+2x^{2}s+12\left(\frac{x}{4}-8\right)\times 2=6048$$

Reiziniet 12 un 2, lai iegūtu 24.

$$24x+2x^{2}s+24\left(\frac{x}{4}-8\right)=6048$$

Izmantojiet distributīvo īpašību, lai reizinātu 24 ar \frac{x}{4}-8.

$$24x+2x^{2}s+24\times \frac{x}{4}-192=6048$$

Noīsiniet lielāko kopējo reizinātāju 4 šeit: 24 un 4.

$$24x+2x^{2}s+6x-192=6048$$

Savelciet 24x un 6x, lai iegūtu 30x.

$$30x+2x^{2}s-192=6048$$

Atņemiet 30x no abām pusēm.

$$2x^{2}s-192=6048-30x$$

Pievienot 192 abās pusēs.

$$2x^{2}s=6048-30x+192$$

Saskaitiet 6048 un 192, lai iegūtu 6240.

$$2x^{2}s=6240-30x$$

Daliet abas puses ar 2x^{2}.

$$\frac{2x^{2}s}{2x^{2}}=\frac{6240-30x}{2x^{2}}$$

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

$$s=\frac{6240-30x}{2x^{2}}$$

Daliet 6240-30x ar 2x^{2}.

$$s=\frac{15\left(208-x\right)}{x^{2}}$$

Atrast x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{15\left(832s+15\right)}-15}{2s}\text{; }x=-\frac{\sqrt{15}\left(\sqrt{832s+15}+\sqrt{15}\right)}{2s}\text{, }&s\neq 0\\x=208\text{, }&s=0\end{matrix}\right,$$

Atrast x

$$\left\{\begin{matrix}x=\frac{\sqrt{15\left(832s+15\right)}-15}{2s}\text{; }x=-\frac{\sqrt{15}\left(\sqrt{832s+15}+\sqrt{15}\right)}{2s}\text{, }&s\neq 0\text{ and }s\geq -\frac{15}{832}\\x=208\text{, }&s=0\end{matrix}\right,$$