Pre-Algebra Examples

$12000 = 0.05 x^{2} - 45 x + 12000$

Step 1

Rewrite the equation as $0.05 x^{2} - 45 x + 12000 = 12000$ .

$0.05 x^{2} - 45 x + 12000 = 12000$

Step 2

Subtract $12000$ from both sides of the equation.

$0.05 x^{2} - 45 x + 12000 - 12000 = 0$

Step 3

Combine the opposite terms in $0.05 x^{2} - 45 x + 12000 - 12000$ .

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Step 3.1

Subtract $12000$ from $12000$ .

$0.05 x^{2} - 45 x + 0 = 0$

Step 3.2

Add $0.05 x^{2} - 45 x$ and $0$ .

$0.05 x^{2} - 45 x = 0$

Step 4

Factor $0.05 x$ out of $0.05 x^{2} - 45 x$ .

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Step 4.1

Factor $0.05 x$ out of $0.05 x^{2}$ .

$0.05 x (x) - 45 x = 0$

Step 4.2

Factor $0.05 x$ out of $- 45 x$ .

$0.05 x (x) + 0.05 x (- 900) = 0$

Step 4.3

Factor $0.05 x$ out of $0.05 x (x) + 0.05 x (- 900)$ .

$0.05 x (x - 900) = 0$

Step 5

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

$x = 0$

$x - 900 = 0$

Step 6

Set $x$ equal to $0$ .

$x = 0$

Step 7

Set $x - 900$ equal to $0$ and solve for $x$ .

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Step 7.1

Set $x - 900$ equal to $0$ .

$x - 900 = 0$

Step 7.2

Add $900$ to both sides of the equation.

$x = 900$

Step 8

The final solution is all the values that make $0.05 x (x - 900) = 0$ true.

$x = 0, 900$