Solve for q q+9/q=-10

$q + \frac{9}{q} = - 10$

Step 1

Find the LCD of the terms in the equation.

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 $q + \frac{9}{q} = - 10$ by $q$ to eliminate the fractions.

Multiply each term in $q + \frac{9}{q} = - 10$ by $q$ .

$q \cdot q + \frac{9}{q} q = - 10 q$

Simplify the left side.

Simplify each term.

Multiply $q$ by $q$ .

$q^{2} + \frac{9}{q} q = - 10 q$

Cancel the common factor of $q$ .

Cancel the common factor.

$q^{2} + \frac{9}{q} q = - 10 q$

Rewrite the expression.

$q^{2} + 9 = - 10 q$

Step 3

Solve the equation.

Add $10 q$ to both sides of the equation.

$q^{2} + 9 + 10 q = 0$

Factor $q^{2} + 9 + 10 q$ using the AC method.

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 $9$ and whose sum is $10$ .

$1, 9$

Write the factored form using these integers.

$(q + 1) (q + 9) = 0$

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

$q + 1 = 0$

$q + 9 = 0$

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

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

$q + 1 = 0$

Subtract $1$ from both sides of the equation.

$q = - 1$

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

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

$q + 9 = 0$

Subtract $9$ from both sides of the equation.

$q = - 9$

The final solution is all the values that make $(q + 1) (q + 9) = 0$ true.

$q = - 1, - 9$

Solve for q q+9/q=-10

Related Questions

Support LCMGCF.com by disabling your adblocker.