Basic Math Examples

$q^{2} = 7 q + 18$

Step 1

Subtract $7 q$ from both sides of the equation.

$q^{2} - 7 q = 18$

Step 2

Subtract $18$ from both sides of the equation.

$q^{2} - 7 q - 18 = 0$

Step 3

Factor $q^{2} - 7 q - 18$ using the AC method.

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Step 3.1

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 $- 18$ and whose sum is $- 7$ .

$- 9, 2$

Step 3.2

Write the factored form using these integers.

$(q - 9) (q + 2) = 0$

Step 4

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

$q - 9 = 0$

$q + 2 = 0$

Step 5

Set $q - 9$ equal to $0$ and solve for $q$ .

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Step 5.1

Set $q - 9$ equal to $0$ .

$q - 9 = 0$

Step 5.2

Add $9$ to both sides of the equation.

$q = 9$

Step 6

Set $q + 2$ equal to $0$ and solve for $q$ .

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Step 6.1

Set $q + 2$ equal to $0$ .

$q + 2 = 0$

Step 6.2

Subtract $2$ from both sides of the equation.

$q = - 2$

Step 7

The final solution is all the values that make $(q - 9) (q + 2) = 0$ true.

$q = 9, - 2$