Question

solve for w.
36w² + 1 = 20w²
write your answer in simplified, rationalized form.
w = or w =

Explanation:

Step1: Move terms with \( w^2 \) to one side

Subtract \( 20w^2 \) and 1 from both sides: \( 36w^2 - 20w^2 = -1 \)
Simplify: \( 16w^2 = -1 \)

Step2: Solve for \( w^2 \)

Divide both sides by 16: \( w^2 = \frac{-1}{16} \)

Step3: Take square root of both sides

\( w = \pm\sqrt{\frac{-1}{16}} \)
Using \( \sqrt{-1} = i \), we get \( w = \pm\frac{i}{4} \)

Answer:

\( w = \frac{i}{4} \) or \( w = -\frac{i}{4} \)