Atrisiniet frac{2sqrt{7}-x}{sqrt{5}}=x/4

$$\frac { 2 \sqrt { 7 } - x } { \sqrt { 5 } } = \frac { x } { 4 }$$

Atrast x

$$x = \frac{32 \sqrt{7} - 8 \sqrt{35}}{11} \approx 3,394127608$$

Lineāra vienādojuma risināšanas darbības

Reiziniet vienādojuma abas puses ar 4.

$$\frac{4}{5}\times 5^{\frac{1}{2}}\left(2\sqrt{7}-x\right)=x$$

Izmantojiet distributīvo īpašību, lai reizinātu \frac{4}{5}\times 5^{\frac{1}{2}} ar 2\sqrt{7}-x.

$$\frac{4}{5}\times 5^{\frac{1}{2}}\times 2\sqrt{7}+\frac{4}{5}\times 5^{\frac{1}{2}}\left(-1\right)x=x$$

Izsakiet \frac{4}{5}\times 2 kā vienu daļskaitli.

$$\frac{4\times 2}{5}\times 5^{\frac{1}{2}}\sqrt{7}+\frac{4}{5}\times 5^{\frac{1}{2}}\left(-1\right)x=x$$

Reiziniet 4 un 2, lai iegūtu 8.

$$\frac{8}{5}\times 5^{\frac{1}{2}}\sqrt{7}+\frac{4}{5}\times 5^{\frac{1}{2}}\left(-1\right)x=x$$

Reiziniet \frac{4}{5} un -1, lai iegūtu -\frac{4}{5}.

$$\frac{8}{5}\times 5^{\frac{1}{2}}\sqrt{7}-\frac{4}{5}\times 5^{\frac{1}{2}}x=x$$

Atņemiet x no abām pusēm.

$$\frac{8}{5}\times 5^{\frac{1}{2}}\sqrt{7}-\frac{4}{5}\times 5^{\frac{1}{2}}x-x=0$$

Atņemiet \frac{8}{5}\times 5^{\frac{1}{2}}\sqrt{7} no abām pusēm. Atņemot nu nulles jebko, iegūst tā noliegumu.

$$-\frac{4}{5}\times 5^{\frac{1}{2}}x-x=-\frac{8}{5}\times 5^{\frac{1}{2}}\sqrt{7}$$

Pārkārtojiet locekļus.

$$-\frac{4}{5}\sqrt{5}x-x=-\frac{8}{5}\sqrt{5}\sqrt{7}$$

Lai reiziniet \sqrt{5} un \sqrt{7}, reiziniet numurus zem kvadrātveida saknes.

$$-\frac{4}{5}\sqrt{5}x-x=-\frac{8}{5}\sqrt{35}$$

Savelciet visus locekļus, kuros ir x.

$$\left(-\frac{4}{5}\sqrt{5}-1\right)x=-\frac{8}{5}\sqrt{35}$$

Vienādojums ir standarta formā.

$$\left(-\frac{4\sqrt{5}}{5}-1\right)x=-\frac{8\sqrt{35}}{5}$$

Daliet abas puses ar -\frac{4}{5}\sqrt{5}-1.

$$\frac{\left(-\frac{4\sqrt{5}}{5}-1\right)x}{-\frac{4\sqrt{5}}{5}-1}=-\frac{\frac{8\sqrt{35}}{5}}{-\frac{4\sqrt{5}}{5}-1}$$

Dalīšana ar -\frac{4}{5}\sqrt{5}-1 atsauc reizināšanu ar -\frac{4}{5}\sqrt{5}-1.

$$x=-\frac{\frac{8\sqrt{35}}{5}}{-\frac{4\sqrt{5}}{5}-1}$$

Daliet -\frac{8\sqrt{35}}{5} ar -\frac{4}{5}\sqrt{5}-1.

$$x=-\frac{8\sqrt{7}\left(\sqrt{5}-4\right)}{11}$$