Issolvi sqrt{2}(x+sqrt{2})=3x-2/sqrt{2}

$$\sqrt { 2 } ( x + \sqrt { 2 } ) = \frac { 3 x - 2 } { \sqrt { 2 } }$$

Solvi għal x

$$x=2\sqrt{2}+2\approx 4.828427125$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Uża l-propjetà distributtiva biex timmultiplika \sqrt{2} b'x+\sqrt{2}.

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

Il-kwadrat ta' \sqrt{2} huwa 2.

$$\sqrt{2}x+2=\frac{3x-2}{\sqrt{2}}$$

Irrazzjonalizza d-denominatur tal-\frac{3x-2}{\sqrt{2}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{2}.

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

Il-kwadrat ta' \sqrt{2} huwa 2.

$$\sqrt{2}x+2=\frac{\left(3x-2\right)\sqrt{2}}{2}$$

Uża l-propjetà distributtiva biex timmultiplika 3x-2 b'\sqrt{2}.

$$\sqrt{2}x+2=\frac{3x\sqrt{2}-2\sqrt{2}}{2}$$

Naqqas \frac{3x\sqrt{2}-2\sqrt{2}}{2} miż-żewġ naħat.

$$\sqrt{2}x+2-\frac{3x\sqrt{2}-2\sqrt{2}}{2}=0$$

Naqqas 2 miż-żewġ naħat. Xi ħaġa mnaqqsa minn żero tagħti numru negattiv.

$$\sqrt{2}x-\frac{3x\sqrt{2}-2\sqrt{2}}{2}=-2$$

Immultiplika ż-żewġ naħat tal-ekwazzjoni b'2.

$$2\sqrt{2}x-\left(3x\sqrt{2}-2\sqrt{2}\right)=-4$$

Biex issib l-oppost ta' 3x\sqrt{2}-2\sqrt{2}, sib l-oppost ta' kull terminu.

$$2\sqrt{2}x-3x\sqrt{2}-\left(-2\sqrt{2}\right)=-4$$

L-oppost ta' -2\sqrt{2} huwa 2\sqrt{2}.

$$2\sqrt{2}x-3x\sqrt{2}+2\sqrt{2}=-4$$

Ikkombina 2\sqrt{2}x u -3x\sqrt{2} biex tikseb -\sqrt{2}x.

$$-\sqrt{2}x+2\sqrt{2}=-4$$

Naqqas 2\sqrt{2} miż-żewġ naħat.

$$-\sqrt{2}x=-4-2\sqrt{2}$$

L-ekwazzjoni hija f'forma standard.

$$\left(-\sqrt{2}\right)x=-2\sqrt{2}-4$$

Iddividi ż-żewġ naħat b'-\sqrt{2}.

$$\frac{\left(-\sqrt{2}\right)x}{-\sqrt{2}}=\frac{-2\sqrt{2}-4}{-\sqrt{2}}$$

Meta tiddividi b'-\sqrt{2} titneħħa l-multiplikazzjoni b'-\sqrt{2}.

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

Iddividi -4-2\sqrt{2} b'-\sqrt{2}.

$$x=2\sqrt{2}+2$$