Solve mu^2=x^2+2u+1

$$\mu ^ { 2 } = x ^ { 2 } + 2 u + 1$$

Solve for u

$$u=\frac{-x^{2}+\mu ^{2}-1}{2}$$

Steps for Solving Linear Equation

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

$$x^{2}+2u+1=\mu ^{2}$$

Subtract x^{2} from both sides.

$$2u+1=\mu ^{2}-x^{2}$$

Subtract 1 from both sides.

$$2u=\mu ^{2}-x^{2}-1$$

The equation is in standard form.

$$2u=-x^{2}+\mu ^{2}-1$$

Divide both sides by 2.

$$\frac{2u}{2}=\frac{-x^{2}+\mu ^{2}-1}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$u=\frac{-x^{2}+\mu ^{2}-1}{2}$$

Solve for x (complex solution)

$$x=-\sqrt{-2u+\mu ^{2}-1}$$

$$x=\sqrt{-2u+\mu ^{2}-1}$$

Solve for x

$$x=\sqrt{-2u+\mu ^{2}-1}$$

$$x=-\sqrt{-2u+\mu ^{2}-1}\text{, }u\leq \frac{\mu ^{2}-1}{2}$$