Question

solve for w.

-12 = w + \frac{27}{w}

if there is more than one solution, separate them with commas
if there is no solution, click on
o solution\.

Explanation:

Step1: Eliminate the denominator

Multiply both sides of the equation \(-12 = w+\frac{27}{w}\) by \(w\) (assuming \(w
eq0\)) to get rid of the fraction. We obtain \(-12w = w^{2}+27\).

Step2: Rearrange into standard quadratic form

Rearrange the equation \(-12w = w^{2}+27\) to the standard quadratic form \(ax^{2}+bx + c = 0\). So we have \(w^{2}+12w + 27=0\).

Step3: Factor the quadratic equation

Factor the quadratic expression \(w^{2}+12w + 27\). We need two numbers that multiply to \(27\) and add up to \(12\). The numbers are \(3\) and \(9\). So, \(w^{2}+12w + 27=(w + 3)(w+9)=0\).

Step4: Solve for \(w\)

Set each factor equal to zero and solve for \(w\).

• For \(w + 3=0\), we get \(w=-3\).
• For \(w + 9=0\), we get \(w=-9\).

We need to check if these solutions are valid (since we multiplied by \(w\) earlier, we must ensure \(w
eq0\), and both \(-3\) and \(-9\) are not zero, so they are valid.

Answer:

\(-9, -3\)