Solve x=sqrt{yp-1}

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

Solve for p

$$p=\frac{x^{2}+1}{y}$$

$$x\geq 0\text{ and }y\neq 0$$

Steps for Solving Radical Equations

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

$$\sqrt{yp-1}=x$$

Square both sides of the equation.

$$yp-1=x^{2}$$

Add 1 to both sides of the equation.

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

Subtracting -1 from itself leaves 0.

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

Subtract -1 from x^{2}.

$$yp=x^{2}+1$$

Divide both sides by y.

$$\frac{yp}{y}=\frac{x^{2}+1}{y}$$

Dividing by y undoes the multiplication by y.

$$p=\frac{x^{2}+1}{y}$$

Solve for p (complex solution)

$$\left\{\begin{matrix}p=\frac{x^{2}+1}{y}\text{, }&y\neq 0\text{ and }\left(x=0\text{ or }arg(x)<\pi \right)\\p\in \mathrm{C}\text{, }&x=i\text{ and }y=0\end{matrix}\right.$$

Solve for x (complex solution)

$$x=\sqrt{py-1}$$

Solve for x

$$x=\sqrt{py-1}$$

$$\left(p<0\text{ or }y\geq \frac{1}{p}\right)\text{ and }\left(p>0\text{ or }y\leq \frac{1}{p}\right)\text{ and }p\neq 0$$