Finite Math Examples

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

Step 1

Subtract $x$ from both sides of the equation.

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

Step 2

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

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Step 2.1

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

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

Step 2.2

Raise $k$ to the power of $1$ .

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

Step 2.3

Factor $k$ out of $k^{1}$ .

$k (x^{2}) + k \cdot 1 = - x$

Step 2.4

Factor $k$ out of $k (x^{2}) + k \cdot 1$ .

$k (x^{2} + 1) = - x$

Step 3

Divide each term in $k (x^{2} + 1) = - x$ by $x^{2} + 1$ and simplify.

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Step 3.1

Divide each term in $k (x^{2} + 1) = - x$ by $x^{2} + 1$ .

$\frac{k (x^{2} + 1)}{x^{2} + 1} = \frac{- x}{x^{2} + 1}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $x^{2} + 1$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{k (x^{2} + 1)}{x^{2} + 1} = \frac{- x}{x^{2} + 1}$

Step 3.2.1.2

Divide $k$ by $1$ .

$k = \frac{- x}{x^{2} + 1}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Move the negative in front of the fraction.

$k = - \frac{x}{x^{2} + 1}$