Solve a * x ^ 2 + bx + c = 0 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$ax^{2}+bx+c=0$$

Solve for a (complex solution)

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

Steps for Solving Linear Equation

Subtract $bx$ from both sides. Anything subtracted from zero gives its negation.

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

Subtract $c$ from both sides.

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

The equation is in standard form.

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

Divide both sides by $x^{2}$.

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

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

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

Divide $-bx-c$ by $x^{2}$.

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

Solve for b (complex solution)

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

Steps for Solving Linear Equation

Subtract $ax^{2}$ from both sides. Anything subtracted from zero gives its negation.

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

Subtract $c$ from both sides.

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

The equation is in standard form.

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

Divide both sides by $x$.

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

Dividing by $x$ undoes the multiplication by $x$.

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

Divide $-ax^{2}-c$ by $x$.

$$b=-ax-\frac{c}{x}$$

Solve for a

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

Steps for Solving Linear Equation

Subtract $bx$ from both sides. Anything subtracted from zero gives its negation.

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

Subtract $c$ from both sides.

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

The equation is in standard form.

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

Divide both sides by $x^{2}$.

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

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

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

Divide $-bx-c$ by $x^{2}$.

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

Solve for b

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

Steps for Solving Linear Equation

Subtract $ax^{2}$ from both sides. Anything subtracted from zero gives its negation.

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

Subtract $c$ from both sides.

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

The equation is in standard form.

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

Divide both sides by $x$.

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

Dividing by $x$ undoes the multiplication by $x$.

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

Divide $-ax^{2}-c$ by $x$.

$$b=-ax-\frac{c}{x}$$