Solve F+g(x)=x^2+x+57

$$F + g ( x ) = x ^ { 2 } + x + 57$$

Solve for g (complex solution)

$$\left\{\begin{matrix}g=\frac{x^{2}+x-F+57}{x}\text{, }&x\neq 0\\g\in \mathrm{C}\text{, }&F=57\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract F from both sides.

$$gx=x^{2}+x+57-F$$

The equation is in standard form.

$$xg=x^{2}+x-F+57$$

Divide both sides by x.

$$\frac{xg}{x}=\frac{x^{2}+x-F+57}{x}$$

Dividing by x undoes the multiplication by x.

$$g=\frac{x^{2}+x-F+57}{x}$$

Solve for g

$$\left\{\begin{matrix}g=\frac{x^{2}+x-F+57}{x}\text{, }&x\neq 0\\g\in \mathrm{R}\text{, }&F=57\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract F from both sides.

$$gx=x^{2}+x+57-F$$

The equation is in standard form.

$$xg=x^{2}+x-F+57$$

Divide both sides by x.

$$\frac{xg}{x}=\frac{x^{2}+x-F+57}{x}$$

Dividing by x undoes the multiplication by x.

$$g=\frac{x^{2}+x-F+57}{x}$$

Solve for F

$$F=x^{2}-gx+x+57$$

Solution Steps

Subtract gx from both sides.

$$F=x^{2}+x+57-gx$$