Solve y=5(sqrt{x-1}-1)

$$y = 5 ( \sqrt { x - 1 } - 1 )$$

Solve for x

$$x=\frac{\left(y+5\right)^{2}+25}{25}$$

$$\frac{y}{5}+1\geq 0$$

Steps for Solving Radical Equations

Use the distributive property to multiply 5 by \sqrt{x-1}-1.

$$y=5\sqrt{x-1}-5$$

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

$$5\sqrt{x-1}-5=y$$

Add 5 to both sides.

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

Divide both sides by 5.

$$\frac{5\sqrt{x-1}}{5}=\frac{y+5}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$\sqrt{x-1}=\frac{y+5}{5}$$

Divide 5+y by 5.

$$\sqrt{x-1}=\frac{y}{5}+1$$

Square both sides of the equation.

$$x-1=\frac{\left(y+5\right)^{2}}{25}$$

Add 1 to both sides of the equation.

$$x-1-\left(-1\right)=\frac{\left(y+5\right)^{2}}{25}-\left(-1\right)$$

Subtracting -1 from itself leaves 0.

$$x=\frac{\left(y+5\right)^{2}}{25}-\left(-1\right)$$

Subtract -1 from \frac{\left(5+y\right)^{2}}{25}.

$$x=\frac{\left(y+5\right)^{2}}{25}+1$$

Solve for x (complex solution)

$$x=\frac{\left(y+5\right)^{2}+25}{25}$$

$$y=-5\text{ or }arg(\frac{y}{5}+1)<\pi$$

Solve for y

$$y=5\left(\sqrt{x-1}-1\right)$$

$$x\geq 1$$