Solve (x-2)^2=2k

$$( x - 2 ) ^ { 2 } = 2 k$$

Solve for k

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

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-2\right)^{2}.

$$x^{2}-4x+4=2k$$

Swap sides so that all variable terms are on the left hand side.

$$2k=x^{2}-4x+4$$

Divide both sides by 2.

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

Dividing by 2 undoes the multiplication by 2.

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

Solve for x (complex solution)

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

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

Solve for x

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

$$x=\sqrt{2k}+2\text{, }k\geq 0$$