Solve y=xsqrt{a+b}

$$y = x \sqrt { a + b }$$

Solve for a

$$\left\{\begin{matrix}a=-b+\left(\frac{y}{x}\right)^{2}\text{, }&\left(y\geq 0\text{ and }x>0\right)\text{ or }\left(y\leq 0\text{ and }x<0\right)\\a\geq -b\text{, }&y=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Radical Equations

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

$$x\sqrt{a+b}=y$$

Divide both sides by x.

$$\frac{x\sqrt{a+b}}{x}=\frac{y}{x}$$

Dividing by x undoes the multiplication by x.

$$\sqrt{a+b}=\frac{y}{x}$$

Square both sides of the equation.

$$a+b=\frac{y^{2}}{x^{2}}$$

Subtract b from both sides of the equation.

$$a+b-b=\frac{y^{2}}{x^{2}}-b$$

Subtracting b from itself leaves 0.

$$a=\frac{y^{2}}{x^{2}}-b$$

Subtract b from \frac{y^{2}}{x^{2}}.

$$a=-b+\frac{y^{2}}{x^{2}}$$

Solve for b

$$\left\{\begin{matrix}b=-a+\left(\frac{y}{x}\right)^{2}\text{, }&\left(y\geq 0\text{ and }x>0\right)\text{ or }\left(y\leq 0\text{ and }x<0\right)\\b\geq -a\text{, }&y=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Radical Equations

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

$$x\sqrt{a+b}=y$$

Divide both sides by x.

$$\frac{x\sqrt{b+a}}{x}=\frac{y}{x}$$

Dividing by x undoes the multiplication by x.

$$\sqrt{b+a}=\frac{y}{x}$$

Square both sides of the equation.

$$b+a=\frac{y^{2}}{x^{2}}$$

Subtract a from both sides of the equation.

$$b+a-a=\frac{y^{2}}{x^{2}}-a$$

Subtracting a from itself leaves 0.

$$b=\frac{y^{2}}{x^{2}}-a$$

Subtract a from \frac{y^{2}}{x^{2}}.

$$b=-a+\frac{y^{2}}{x^{2}}$$

Solve for a (complex solution)

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

Solve for b (complex solution)

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