Solve v=sqrt{1-t/4}

$$v = \sqrt { \frac { 1 - t } { 4 } }$$

Solve for t

$$t=1-4v^{2}$$

$$v\geq 0$$

Steps for Solving Radical Equations

Divide each term of 1-t by 4 to get \frac{1}{4}-\frac{1}{4}t.

$$v=\sqrt{\frac{1}{4}-\frac{1}{4}t}$$

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

$$\sqrt{\frac{1}{4}-\frac{1}{4}t}=v$$

Square both sides of the equation.

$$-\frac{1}{4}t+\frac{1}{4}=v^{2}$$

Subtract \frac{1}{4} from both sides of the equation.

$$-\frac{1}{4}t+\frac{1}{4}-\frac{1}{4}=v^{2}-\frac{1}{4}$$

Subtracting \frac{1}{4} from itself leaves 0.

$$-\frac{1}{4}t=v^{2}-\frac{1}{4}$$

Multiply both sides by -4.

$$\frac{-\frac{1}{4}t}{-\frac{1}{4}}=\frac{v^{2}-\frac{1}{4}}{-\frac{1}{4}}$$

Dividing by -\frac{1}{4} undoes the multiplication by -\frac{1}{4}.

$$t=\frac{v^{2}-\frac{1}{4}}{-\frac{1}{4}}$$

Divide v^{2}-\frac{1}{4} by -\frac{1}{4} by multiplying v^{2}-\frac{1}{4} by the reciprocal of -\frac{1}{4}.

$$t=1-4v^{2}$$

Solve for t (complex solution)

$$t=1-4v^{2}$$

$$arg(v)<\pi \text{ or }v=0$$

Solve for v (complex solution)

$$v=\frac{\sqrt{1-t}}{2}$$

Solve for v

$$v=\frac{\sqrt{1-t}}{2}$$

$$t\leq 1$$