Algebra Examples

$q + \frac{5}{q} = - 6$

Step 1

Find the LCD of the terms in the equation.

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Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$1, q, 1$

The LCM of one and any expression is the expression.

$q$

Step 2

Multiply each term in $q + \frac{5}{q} = - 6$ by $q$ to eliminate the fractions.

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Multiply each term in $q + \frac{5}{q} = - 6$ by $q$ .

$q \cdot q + \frac{5}{q} q = - 6 q$

Simplify the left side.

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Simplify each term.

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Multiply $q$ by $q$ .

$q^{2} + \frac{5}{q} q = - 6 q$

Cancel the common factor of $q$ .

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Cancel the common factor.

$q^{2} + \frac{5}{q} q = - 6 q$

Rewrite the expression.

$q^{2} + 5 = - 6 q$

Step 3

Solve the equation.

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Add $6 q$ to both sides of the equation.

$q^{2} + 5 + 6 q = 0$

Factor $q^{2} + 5 + 6 q$ using the AC method.

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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 $5$ and whose sum is $6$ .

$1, 5$

Write the factored form using these integers.

$(q + 1) (q + 5) = 0$

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

$q + 1 = 0$

$q + 5 = 0$

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

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

$q + 1 = 0$

Subtract $1$ from both sides of the equation.

$q = - 1$

Set $q + 5$ equal to $0$ and solve for $q$ .

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Set $q + 5$ equal to $0$ .

$q + 5 = 0$

Subtract $5$ from both sides of the equation.

$q = - 5$

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

$q = - 1, - 5$