Solve y=1/2sqrt{x+1}-5

$$y = \frac { 1 } { 2 } \sqrt { x + 1 } - 5$$

Solve for x

$$x=\left(2y+9\right)\left(2y+11\right)$$

$$2y+10\geq 0$$

Steps for Solving Radical Equations

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

$$\frac{1}{2}\sqrt{x+1}-5=y$$

Add 5 to both sides.

$$\frac{1}{2}\sqrt{x+1}=y+5$$

Multiply both sides by 2.

$$\frac{\frac{1}{2}\sqrt{x+1}}{\frac{1}{2}}=\frac{y+5}{\frac{1}{2}}$$

Dividing by \frac{1}{2} undoes the multiplication by \frac{1}{2}.

$$\sqrt{x+1}=\frac{y+5}{\frac{1}{2}}$$

Divide y+5 by \frac{1}{2} by multiplying y+5 by the reciprocal of \frac{1}{2}.

$$\sqrt{x+1}=2y+10$$

Square both sides of the equation.

$$x+1=4\left(y+5\right)^{2}$$

Subtract 1 from both sides of the equation.

$$x+1-1=4\left(y+5\right)^{2}-1$$

Subtracting 1 from itself leaves 0.

$$x=4\left(y+5\right)^{2}-1$$

Subtract 1 from 4\left(5+y\right)^{2}.

$$x=4y^{2}+40y+99$$

Solve for x (complex solution)

$$x=\left(2y+9\right)\left(2y+11\right)$$

$$y=-5\text{ or }arg(2y+10)<\pi$$

Solve for y (complex solution)

$$y=\frac{\sqrt{x+1}-10}{2}$$

Solve for y

$$y=\frac{\sqrt{x+1}-10}{2}$$

$$x\geq -1$$