Atrisiniet x^2+2sqrt{2}kx+18=0

$${ x }^{ 2 } +2 \sqrt{ 2 } kx+18=0$$

Atrast k

$$k=-\frac{\sqrt{2}\left(x^{2}+18\right)}{4x}$$

$$x\neq 0$$

Lineāra vienādojuma risināšanas darbības

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

$$2\sqrt{2}kx+18=-x^{2}$$

Atņemiet 18 no abām pusēm.

$$2\sqrt{2}kx=-x^{2}-18$$

Vienādojums ir standarta formā.

$$2\sqrt{2}xk=-x^{2}-18$$

Daliet abas puses ar 2\sqrt{2}x.

$$\frac{2\sqrt{2}xk}{2\sqrt{2}x}=\frac{-x^{2}-18}{2\sqrt{2}x}$$

Dalīšana ar 2\sqrt{2}x atsauc reizināšanu ar 2\sqrt{2}x.

$$k=\frac{-x^{2}-18}{2\sqrt{2}x}$$

Daliet -x^{2}-18 ar 2\sqrt{2}x.

$$k=-\frac{\sqrt{2}\left(x^{2}+18\right)}{4x}$$

Atrast x (complex solution)

$$x=\sqrt{2}\left(\sqrt{k^{2}-9}-k\right)$$

$$x=\sqrt{2}\left(-\sqrt{k^{2}-9}-k\right)$$

Atrast x

$$x=\sqrt{2}\left(\sqrt{k^{2}-9}-k\right)$$

$$x=\sqrt{2}\left(-\sqrt{k^{2}-9}-k\right)\text{, }|k|\geq 3$$