Finite Math Examples

$0 = q^{2} + 110 q - 6000$

Step 1

Move all the expressions to the left side of the equation.

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Step 1.1

Subtract $q^{2}$ from both sides of the equation.

$- q^{2} = 110 q - 6000$

Step 1.2

Subtract $110 q$ from both sides of the equation.

$- q^{2} - 110 q = - 6000$

Step 1.3

Add $6000$ to both sides of the equation.

$- q^{2} - 110 q + 6000 = 0$

Step 2

Factor $- 1$ out of $- q^{2} - 110 q + 6000$ .

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Step 2.1

Factor $- 1$ out of $- q^{2}$ .

$- (q^{2}) - 110 q + 6000 = 0$

Step 2.2

Factor $- 1$ out of $- 110 q$ .

$- (q^{2}) - (110 q) + 6000 = 0$

Step 2.3

Rewrite $6000$ as $- 1 (- 6000)$ .

$- (q^{2}) - (110 q) - 1 \cdot - 6000 = 0$

Step 2.4

Factor $- 1$ out of $- (q^{2}) - (110 q)$ .

$- (q^{2} + 110 q) - 1 \cdot - 6000 = 0$

Step 2.5

Factor $- 1$ out of $- (q^{2} + 110 q) - 1 (- 6000)$ .

$- (q^{2} + 110 q - 6000) = 0$

Step 3

Factor.

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Step 3.1

Factor $q^{2} + 110 q - 6000$ using the AC method.

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Step 3.1.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 6000$ and whose sum is $110$ .

$- 40, 150$

Step 3.1.2

Write the factored form using these integers.

$- ((q - 40) (q + 150)) = 0$

Step 3.2

Remove unnecessary parentheses.

$- (q - 40) (q + 150) = 0$