Question

homework 9: section 2.5
score: 50/180 answered: 5/28
question 6
solve the equation: ( m - 9 = -\frac{18}{m} )
answer: ( m = )
write your answers as a list of integers or reduced fractions, with your answers separated by (a) comma(s).
for example, if you get 4 and ( -\frac{2}{3} ) as your answers, then enter 4,-2/3 in the box.
question help: message instructor

Explanation:

Step1: Eliminate the denominator

Multiply both sides of the equation \( m - 9 = -\frac{18}{m} \) by \( m \) (assuming \( m
eq0 \)) to get \( m(m - 9)=- 18 \).
Expand the left - hand side: \( m^{2}-9m=-18 \).

Step2: Rearrange into standard quadratic form

Rearrange the equation \( m^{2}-9m = - 18 \) to the standard quadratic form \( ax^{2}+bx + c = 0 \).
We get \( m^{2}-9m + 18=0 \).

Step3: Factor the quadratic equation

Factor the quadratic expression \( m^{2}-9m + 18 \).
We need to find two numbers that multiply to \( 18 \) and add up to \( - 9 \). The numbers are \( - 3 \) and \( - 6 \).
So, \( m^{2}-9m + 18=(m - 3)(m - 6)=0 \).

Step4: Solve for m

Set each factor equal to zero:

• If \( m - 3=0 \), then \( m = 3 \).
• If \( m - 6=0 \), then \( m = 6 \).

We need to check if these solutions are valid (since we multiplied by \( m \) earlier, we need to make sure \( m
eq0 \), and both \( 3
eq0 \) and \( 6
eq0 \)).

Answer:

3,6