Linear Algebra Examples

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

Step 1

Subtract $k x$ from both sides of the equation.

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

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

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

Step 3

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

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Step 3.1

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

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

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.

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

Step 3.2.1.2

Divide $m$ by $1$ .

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

Step 3.3

Simplify the right side.

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Step 3.3.1

Move the negative in front of the fraction.

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

Step 4

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$