Solve ax^2+4x+k=0

$$a x ^ { 2 } + 4 x + k = 0$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{4x+k}{x^{2}}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&x=0\text{ and }k=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 4x from both sides. Anything subtracted from zero gives its negation.

$$ax^{2}+k=-4x$$

Subtract k from both sides.

$$ax^{2}=-4x-k$$

The equation is in standard form.

$$x^{2}a=-4x-k$$

Divide both sides by x^{2}.

$$\frac{x^{2}a}{x^{2}}=\frac{-4x-k}{x^{2}}$$

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

$$a=\frac{-4x-k}{x^{2}}$$

Divide -4x-k by x^{2}.

$$a=-\frac{4x+k}{x^{2}}$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{4x+k}{x^{2}}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&x=0\text{ and }k=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 4x from both sides. Anything subtracted from zero gives its negation.

$$ax^{2}+k=-4x$$

Subtract k from both sides.

$$ax^{2}=-4x-k$$

The equation is in standard form.

$$x^{2}a=-4x-k$$

Divide both sides by x^{2}.

$$\frac{x^{2}a}{x^{2}}=\frac{-4x-k}{x^{2}}$$

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

$$a=\frac{-4x-k}{x^{2}}$$

Divide -4x-k by x^{2}.

$$a=-\frac{4x+k}{x^{2}}$$

Solve for k

$$k=-x\left(ax+4\right)$$