Solve x=frac{-bpmsqrt{b^2}-4ac}{2a}

$$x = \frac { - b \pm \sqrt { b ^ { 2 } } - 4 a c } { 2 a }$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{-b±\sqrt{b^{2}}}{2\left(x+2c\right)}\text{, }&-b±\sqrt{b^{2}}\neq 0\text{ and }x\neq -2c\\a\neq 0\text{, }&-b±\sqrt{b^{2}}=0\text{ and }x=-2c\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2a.

$$x\times 2a=-b±\sqrt{b^{2}}-4ac$$

Add 4ac to both sides.

$$x\times 2a+4ac=-b±\sqrt{b^{2}}$$

Combine all terms containing a.

$$\left(x\times 2+4c\right)a=-b±\sqrt{b^{2}}$$

The equation is in standard form.

$$\left(2x+4c\right)a=-b±\sqrt{b^{2}}$$

Divide both sides by 2x+4c.

$$\frac{\left(2x+4c\right)a}{2x+4c}=\frac{-b±\sqrt{b^{2}}}{2x+4c}$$

Dividing by 2x+4c undoes the multiplication by 2x+4c.

$$a=\frac{-b±\sqrt{b^{2}}}{2x+4c}$$

Divide -b±\sqrt{b^{2}} by 2x+4c.

$$a=\frac{-b±\sqrt{b^{2}}}{2\left(x+2c\right)}$$

Variable a cannot be equal to 0.

$$a=\frac{-b±\sqrt{b^{2}}}{2\left(x+2c\right)}\text{, }a\neq 0$$

Solve for a

$$\left\{\begin{matrix}a=\frac{-b±|b|}{2\left(x+2c\right)}\text{, }&-b±|b|\neq 0\text{ and }x\neq -2c\\a\neq 0\text{, }&-b±|b|=0\text{ and }x=-2c\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2a.

$$x\times 2a=-b±\sqrt{b^{2}}-4ac$$

Add 4ac to both sides.

$$x\times 2a+4ac=-b±\sqrt{b^{2}}$$

Combine all terms containing a.

$$\left(x\times 2+4c\right)a=-b±\sqrt{b^{2}}$$

The equation is in standard form.

$$\left(2x+4c\right)a=-b±\sqrt{b^{2}}$$

Divide both sides by 2x+4c.

$$\frac{\left(2x+4c\right)a}{2x+4c}=\frac{-b±|b|}{2x+4c}$$

Dividing by 2x+4c undoes the multiplication by 2x+4c.

$$a=\frac{-b±|b|}{2x+4c}$$

Divide -b±|b| by 2x+4c.

$$a=\frac{-b±|b|}{2\left(x+2c\right)}$$

Variable a cannot be equal to 0.

$$a=\frac{-b±|b|}{2\left(x+2c\right)}\text{, }a\neq 0$$