Solve 58=ax^2+bx+c

$$58 = a x ^ { 2 } + b x + c$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{bx+c-58}{x^{2}}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&c=58\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$ax^{2}+bx+c=58$$

Subtract bx from both sides.

$$ax^{2}+c=58-bx$$

Subtract c from both sides.

$$ax^{2}=58-bx-c$$

The equation is in standard form.

$$x^{2}a=58-c-bx$$

Divide both sides by x^{2}.

$$\frac{x^{2}a}{x^{2}}=\frac{58-c-bx}{x^{2}}$$

Dividing by x^{2} undoes the multiplication by x^{2}.

$$a=\frac{58-c-bx}{x^{2}}$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=-\frac{ax^{2}+c-58}{x}\text{, }&x\neq 0\\b\in \mathrm{C}\text{, }&c=58\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$ax^{2}+bx+c=58$$

Subtract ax^{2} from both sides.

$$bx+c=58-ax^{2}$$

Subtract c from both sides.

$$bx=58-ax^{2}-c$$

Reorder the terms.

$$bx=-ax^{2}-c+58$$

The equation is in standard form.

$$xb=58-c-ax^{2}$$

Divide both sides by x.

$$\frac{xb}{x}=\frac{58-c-ax^{2}}{x}$$

Dividing by x undoes the multiplication by x.

$$b=\frac{58-c-ax^{2}}{x}$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{bx+c-58}{x^{2}}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&c=58\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$ax^{2}+bx+c=58$$

Subtract bx from both sides.

$$ax^{2}+c=58-bx$$

Subtract c from both sides.

$$ax^{2}=58-bx-c$$

The equation is in standard form.

$$x^{2}a=58-c-bx$$

Divide both sides by x^{2}.

$$\frac{x^{2}a}{x^{2}}=\frac{58-c-bx}{x^{2}}$$

Dividing by x^{2} undoes the multiplication by x^{2}.

$$a=\frac{58-c-bx}{x^{2}}$$

Solve for b

$$\left\{\begin{matrix}b=-\frac{ax^{2}+c-58}{x}\text{, }&x\neq 0\\b\in \mathrm{R}\text{, }&c=58\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$ax^{2}+bx+c=58$$

Subtract ax^{2} from both sides.

$$bx+c=58-ax^{2}$$

Subtract c from both sides.

$$bx=58-ax^{2}-c$$

Reorder the terms.

$$bx=-ax^{2}-c+58$$

The equation is in standard form.

$$xb=58-c-ax^{2}$$

Divide both sides by x.

$$\frac{xb}{x}=\frac{58-c-ax^{2}}{x}$$

Dividing by x undoes the multiplication by x.

$$b=\frac{58-c-ax^{2}}{x}$$