Solve sqrt{5x+1}+t=1

$$\sqrt { 5 x + 1 } + t = 1$$

Solve for x

$$x=-\frac{t\left(2-t\right)}{5}$$

$$1-t\geq 0$$

Steps for Solving Radical Equations

Subtract t from both sides of the equation.

$$\sqrt{5x+1}+t-t=1-t$$

Subtracting t from itself leaves 0.

$$\sqrt{5x+1}=1-t$$

Square both sides of the equation.

$$5x+1=\left(1-t\right)^{2}$$

Subtract 1 from both sides of the equation.

$$5x+1-1=\left(1-t\right)^{2}-1$$

Subtracting 1 from itself leaves 0.

$$5x=\left(1-t\right)^{2}-1$$

Subtract 1 from \left(-t+1\right)^{2}.

$$5x=t^{2}-2t$$

Divide both sides by 5.

$$\frac{5x}{5}=\frac{t^{2}-2t}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$x=\frac{t^{2}-2t}{5}$$

Divide -2t+t^{2} by 5.

$$x=\frac{t\left(t-2\right)}{5}$$

Solve for t (complex solution)

$$t=-\sqrt{5x+1}+1$$

Solve for x (complex solution)

$$x=-\frac{t\left(2-t\right)}{5}$$

$$t=1\text{ or }arg(1-t)<\pi$$

Solve for t

$$t=-\sqrt{5x+1}+1$$

$$x\geq -\frac{1}{5}$$