Finite Math Examples

$f (x) = - 5 x^{2} - 5 x$

Step 1

Set $- 5 x^{2} - 5 x$ equal to $0$ .

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

Step 2

Solve for $x$ .

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Step 2.1

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

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Step 2.1.1

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

$- 5 x \cdot x - 5 x = 0$

Step 2.1.2

Factor $- 5 x$ out of $- 5 x$ .

$- 5 x \cdot x - 5 x \cdot 1 = 0$

Step 2.1.3

Factor $- 5 x$ out of $- 5 x (x) - 5 x (1)$ .

$- 5 x (x + 1) = 0$

Step 2.2

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

$x = 0$

$x + 1 = 0$

Step 2.3

Set $x$ equal to $0$ .

$x = 0$

Step 2.4

Set $x + 1$ equal to $0$ and solve for $x$ .

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Step 2.4.1

Set $x + 1$ equal to $0$ .

$x + 1 = 0$

Step 2.4.2

Subtract $1$ from both sides of the equation.

$x = - 1$

Step 2.5

The final solution is all the values that make $- 5 x (x + 1) = 0$ true.

$x = 0, - 1$

Step 3