Solve a_{1}x^2+2b_{1}x+c_{1}=0

$$a _ { 1 } x ^ { 2 } + 2 b _ { 1 } x + c _ { 1 } = 0$$

Solve for a_1 (complex solution)

$$\left\{\begin{matrix}a_{1}=-\frac{2b_{1}x+c_{1}}{x^{2}}\text{, }&x\neq 0\\a_{1}\in \mathrm{C}\text{, }&c_{1}=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 2b_{1}x from both sides. Anything subtracted from zero gives its negation.

$$a_{1}x^{2}+c_{1}=-2b_{1}x$$

Subtract c_{1} from both sides.

$$a_{1}x^{2}=-2b_{1}x-c_{1}$$

The equation is in standard form.

$$x^{2}a_{1}=-2b_{1}x-c_{1}$$

Divide both sides by x^{2}.

$$\frac{x^{2}a_{1}}{x^{2}}=\frac{-2b_{1}x-c_{1}}{x^{2}}$$

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

$$a_{1}=\frac{-2b_{1}x-c_{1}}{x^{2}}$$

Divide -2b_{1}x-c_{1} by x^{2}.

$$a_{1}=-\frac{2b_{1}x+c_{1}}{x^{2}}$$

Solve for b_1 (complex solution)

$$\left\{\begin{matrix}b_{1}=-\frac{a_{1}x^{2}+c_{1}}{2x}\text{, }&x\neq 0\\b_{1}\in \mathrm{C}\text{, }&c_{1}=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract a_{1}x^{2} from both sides. Anything subtracted from zero gives its negation.

$$2b_{1}x+c_{1}=-a_{1}x^{2}$$

Subtract c_{1} from both sides.

$$2b_{1}x=-a_{1}x^{2}-c_{1}$$

The equation is in standard form.

$$2xb_{1}=-a_{1}x^{2}-c_{1}$$

Divide both sides by 2x.

$$\frac{2xb_{1}}{2x}=\frac{-a_{1}x^{2}-c_{1}}{2x}$$

Dividing by 2x undoes the multiplication by 2x.

$$b_{1}=\frac{-a_{1}x^{2}-c_{1}}{2x}$$

Divide -a_{1}x^{2}-c_{1} by 2x.

$$b_{1}=-\frac{a_{1}x}{2}-\frac{c_{1}}{2x}$$

Solve for a_1

$$\left\{\begin{matrix}a_{1}=-\frac{2b_{1}x+c_{1}}{x^{2}}\text{, }&x\neq 0\\a_{1}\in \mathrm{R}\text{, }&c_{1}=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 2b_{1}x from both sides. Anything subtracted from zero gives its negation.

$$a_{1}x^{2}+c_{1}=-2b_{1}x$$

Subtract c_{1} from both sides.

$$a_{1}x^{2}=-2b_{1}x-c_{1}$$

The equation is in standard form.

$$x^{2}a_{1}=-2b_{1}x-c_{1}$$

Divide both sides by x^{2}.

$$\frac{x^{2}a_{1}}{x^{2}}=\frac{-2b_{1}x-c_{1}}{x^{2}}$$

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

$$a_{1}=\frac{-2b_{1}x-c_{1}}{x^{2}}$$

Divide -2b_{1}x-c_{1} by x^{2}.

$$a_{1}=-\frac{2b_{1}x+c_{1}}{x^{2}}$$

Solve for b_1

$$\left\{\begin{matrix}b_{1}=-\frac{a_{1}x^{2}+c_{1}}{2x}\text{, }&x\neq 0\\b_{1}\in \mathrm{R}\text{, }&c_{1}=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract a_{1}x^{2} from both sides. Anything subtracted from zero gives its negation.

$$2b_{1}x+c_{1}=-a_{1}x^{2}$$

Subtract c_{1} from both sides.

$$2b_{1}x=-a_{1}x^{2}-c_{1}$$

The equation is in standard form.

$$2xb_{1}=-a_{1}x^{2}-c_{1}$$

Divide both sides by 2x.

$$\frac{2xb_{1}}{2x}=\frac{-a_{1}x^{2}-c_{1}}{2x}$$

Dividing by 2x undoes the multiplication by 2x.

$$b_{1}=\frac{-a_{1}x^{2}-c_{1}}{2x}$$

Divide -a_{1}x^{2}-c_{1} by 2x.

$$b_{1}=-\frac{a_{1}x}{2}-\frac{c_{1}}{2x}$$