Solve (h-1)^2=2n

$$( h - 1 ) ^ { 2 } = 2 n$$

Solve for n

$$n=\frac{\left(h-1\right)^{2}}{2}$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(h-1\right)^{2}.

$$h^{2}-2h+1=2n$$

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

$$2n=h^{2}-2h+1$$

Divide both sides by 2.

$$\frac{2n}{2}=\frac{\left(h-1\right)^{2}}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$n=\frac{\left(h-1\right)^{2}}{2}$$

Solve for h (complex solution)

$$h=-\sqrt{2n}+1$$

$$h=\sqrt{2n}+1$$

Solve for h

$$h=-\sqrt{2n}+1$$

$$h=\sqrt{2n}+1\text{, }n\geq 0$$