Solve sqrt{u}+y=2v

$$\sqrt { u } + y = 2 v$$

Solve for v (complex solution)

$$v=\frac{y+\sqrt{u}}{2}$$

Steps for Solving Linear Equation

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

$$2v=\sqrt{u}+y$$

The equation is in standard form.

$$2v=y+\sqrt{u}$$

Divide both sides by 2.

$$\frac{2v}{2}=\frac{y+\sqrt{u}}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$v=\frac{y+\sqrt{u}}{2}$$

Solve for u

$$u=\left(y-2v\right)^{2}$$

$$-\left(y-2v\right)\geq 0$$

Steps for Solving Radical Equations

Subtract y from both sides of the equation.

$$\sqrt{u}+y-y=2v-y$$

Subtracting y from itself leaves 0.

$$\sqrt{u}=2v-y$$

Square both sides of the equation.

$$u=\left(2v-y\right)^{2}$$

Solve for v

$$v=\frac{y+\sqrt{u}}{2}$$

$$u\geq 0$$

Steps for Solving Linear Equation

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

$$2v=\sqrt{u}+y$$

The equation is in standard form.

$$2v=y+\sqrt{u}$$

Divide both sides by 2.

$$\frac{2v}{2}=\frac{y+\sqrt{u}}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$v=\frac{y+\sqrt{u}}{2}$$

Solve for u (complex solution)

$$u=\left(y-2v\right)^{2}$$

$$y=2v\text{ or }arg(y-2v)\geq \pi$$