Basic Math Examples

$\frac{1}{9} q^{2} - q + 2 = 0$

Step 1

Combine $\frac{1}{9}$ and $q^{2}$ .

$\frac{q^{2}}{9} - q + 2 = 0$

Step 2

Multiply each term in $\frac{q^{2}}{9} - q + 2 = 0$ by $9$ to eliminate the fractions.

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Step 2.1

Multiply each term in $\frac{q^{2}}{9} - q + 2 = 0$ by $9$ .

$\frac{q^{2}}{9} \cdot 9 - q \cdot 9 + 2 \cdot 9 = 0 \cdot 9$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify each term.

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Step 2.2.1.1

Cancel the common factor of $9$ .

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Step 2.2.1.1.1

Cancel the common factor.

$\frac{q^{2}}{9} \cdot 9 - q \cdot 9 + 2 \cdot 9 = 0 \cdot 9$

Step 2.2.1.1.2

Rewrite the expression.

$q^{2} - q \cdot 9 + 2 \cdot 9 = 0 \cdot 9$

Step 2.2.1.2

Multiply $9$ by $- 1$ .

$q^{2} - 9 q + 2 \cdot 9 = 0 \cdot 9$

Step 2.2.1.3

Multiply $2$ by $9$ .

$q^{2} - 9 q + 18 = 0 \cdot 9$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply $0$ by $9$ .

$q^{2} - 9 q + 18 = 0$

Step 3

Factor $q^{2} - 9 q + 18$ 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 $- 9$ .

$- 6, - 3$

Step 3.2

Write the factored form using these integers.

$(q - 6) (q - 3) = 0$

Step 4

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

$q - 6 = 0$

$q - 3 = 0$

Step 5

Set $q - 6$ equal to $0$ and solve for $q$ .

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Step 5.1

Set $q - 6$ equal to $0$ .

$q - 6 = 0$

Step 5.2

Add $6$ to both sides of the equation.

$q = 6$

Step 6

Set $q - 3$ equal to $0$ and solve for $q$ .

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Step 6.1

Set $q - 3$ equal to $0$ .

$q - 3 = 0$

Step 6.2

Add $3$ to both sides of the equation.

$q = 3$

Step 7

The final solution is all the values that make $(q - 6) (q - 3) = 0$ true.

$q = 6, 3$