Solve for k kx^2+x+100k=0

$k x^{2} + x + 100 k = 0$

Subtract $x$ from both sides of the equation.

$k x^{2} + 100 k = - x$

Factor $k$ out of $k x^{2} + 100 k$ .

Factor $k$ out of $k x^{2}$ .

$k (x^{2}) + 100 k = - x$

Factor $k$ out of $100 k$ .

$k (x^{2}) + k \cdot 100 = - x$

Factor $k$ out of $k (x^{2}) + k \cdot 100$ .

$k (x^{2} + 100) = - x$

Divide each term in $k (x^{2} + 100) = - x$ by $x^{2} + 100$ and simplify.

Divide each term in $k (x^{2} + 100) = - x$ by $x^{2} + 100$ .

$\frac{k (x^{2} + 100)}{x^{2} + 100} = \frac{- x}{x^{2} + 100}$

Simplify the left side.

Cancel the common factor of $x^{2} + 100$ .

Cancel the common factor.

$\frac{k (x^{2} + 100)}{x^{2} + 100} = \frac{- x}{x^{2} + 100}$

Divide $k$ by $1$ .

$k = \frac{- x}{x^{2} + 100}$

Simplify the right side.

Move the negative in front of the fraction.

$k = - \frac{x}{x^{2} + 100}$