Solve f:y=sqrt{(-x^2-3x+10)}

$$f : y = \sqrt { ( - x ^ { 2 } - 3 x + 10 ) }$$

Solve for f (complex solution)

$$f=y\sqrt{\left(2-x\right)\left(x+5\right)}$$

$$y\neq 0$$

Steps for Solving Linear Equation

The equation is in standard form.

$$\frac{1}{y}f=\sqrt{10-3x-x^{2}}$$

Divide both sides by y^{-1}.

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

Dividing by y^{-1} undoes the multiplication by y^{-1}.

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

Divide \sqrt{\left(2-x\right)\left(5+x\right)} by y^{-1}.

$$f=y\sqrt{\left(2-x\right)\left(x+5\right)}$$

Solve for f

$$f=y\sqrt{\left(2-x\right)\left(x+5\right)}$$

$$y\neq 0\text{ and }x\geq -5\text{ and }x\leq 2$$

Steps for Solving Linear Equation

The equation is in standard form.

$$\frac{1}{y}f=\sqrt{10-3x-x^{2}}$$

Divide both sides by y^{-1}.

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

Dividing by y^{-1} undoes the multiplication by y^{-1}.

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

Divide \sqrt{\left(2-x\right)\left(5+x\right)} by y^{-1}.

$$f=y\sqrt{\left(2-x\right)\left(x+5\right)}$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{49y^{4}-4\left(fy\right)^{2}}}{2y^{2}}-\frac{3}{2}$$

$$x=\frac{\sqrt{49y^{4}-4\left(fy\right)^{2}}}{2y^{2}}-\frac{3}{2}\text{, }y\neq 0\text{ and }\left(|arg(\sqrt{\left(\frac{f}{y}\right)^{2}}y)-arg(f)|<\pi \text{ or }f=0\right)$$

Solve for x

$$x=-\frac{\sqrt{49y^{2}-4f^{2}}}{2y}-\frac{3}{2}$$

$$x=\frac{\sqrt{49y^{2}-4f^{2}}}{2y}-\frac{3}{2}\text{, }f\neq -\frac{7y}{2}\text{ and }y\neq 0\text{ and }f\leq \frac{7|y|}{2}\text{ and }f\geq -\frac{7|y|}{2}\text{ and }\left(f\geq \frac{7y}{2}\text{ or }f\geq 0\right)\text{ and }\left(f\leq 0\text{ or }f\leq \frac{7y}{2}\right)$$