Solve nP(x)=-x^2+14x+57

$$n P ( x ) = - x ^ { 2 } + 14 x + 57$$

Solve for P (complex solution)

$$\left\{\begin{matrix}P=-\frac{x^{2}-14x-57}{nx}\text{, }&x\neq 0\text{ and }n\neq 0\\P\in \mathrm{C}\text{, }&\left(x=7-\sqrt{106}\text{ or }x=\sqrt{106}+7\right)\text{ and }n=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$nxP=57+14x-x^{2}$$

Divide both sides by nx.

$$\frac{nxP}{nx}=\frac{57+14x-x^{2}}{nx}$$

Dividing by nx undoes the multiplication by nx.

$$P=\frac{57+14x-x^{2}}{nx}$$

Solve for n (complex solution)

$$\left\{\begin{matrix}n=-\frac{x^{2}-14x-57}{Px}\text{, }&x\neq 0\text{ and }P\neq 0\\n\in \mathrm{C}\text{, }&\left(x=7-\sqrt{106}\text{ or }x=\sqrt{106}+7\right)\text{ and }P=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$Pxn=57+14x-x^{2}$$

Divide both sides by Px.

$$\frac{Pxn}{Px}=\frac{57+14x-x^{2}}{Px}$$

Dividing by Px undoes the multiplication by Px.

$$n=\frac{57+14x-x^{2}}{Px}$$

Solve for P

$$\left\{\begin{matrix}P=-\frac{x^{2}-14x-57}{nx}\text{, }&x\neq 0\text{ and }n\neq 0\\P\in \mathrm{R}\text{, }&\left(x=7-\sqrt{106}\text{ or }x=\sqrt{106}+7\right)\text{ and }n=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$nxP=57+14x-x^{2}$$

Divide both sides by nx.

$$\frac{nxP}{nx}=\frac{57+14x-x^{2}}{nx}$$

Dividing by nx undoes the multiplication by nx.

$$P=\frac{57+14x-x^{2}}{nx}$$

Solve for n

$$\left\{\begin{matrix}n=-\frac{x^{2}-14x-57}{Px}\text{, }&x\neq 0\text{ and }P\neq 0\\n\in \mathrm{R}\text{, }&\left(x=7-\sqrt{106}\text{ or }x=\sqrt{106}+7\right)\text{ and }P=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$Pxn=57+14x-x^{2}$$

Divide both sides by Px.

$$\frac{Pxn}{Px}=\frac{57+14x-x^{2}}{Px}$$

Dividing by Px undoes the multiplication by Px.

$$n=\frac{57+14x-x^{2}}{Px}$$