Linear Algebra Examples

$x^{2} + 5 x = 0$

Step 1

Factor $x$ out of $x^{2} + 5 x$ .

Tap for more steps...

Step 1.1

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

$x \cdot x + 5 x = 0$

Step 1.2

Factor $x$ out of $5 x$ .

$x \cdot x + x \cdot 5 = 0$

Step 1.3

Factor $x$ out of $x \cdot x + x \cdot 5$ .

$x (x + 5) = 0$

Step 2

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$x + 5 = 0$

Step 3

Set $x$ equal to $0$ .

$x = 0$

Step 4

Set $x + 5$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 4.1

Set $x + 5$ equal to $0$ .

$x + 5 = 0$

Step 4.2

Subtract $5$ from both sides of the equation.

$x = - 5$

Step 5

The final solution is all the values that make $x (x + 5) = 0$ true.

$x = 0, - 5$

Step 6

The domain is the set of all valid $x$ values.

${x | x = 0, - 5}$

Step 7