Question

11 - 3r² = -49

Explanation:

Step1: Subtract 11 from both sides

To isolate the term with \( r^2 \), we subtract 11 from both sides of the equation \( 11 - 3r^2 = -49 \).
\[
11 - 3r^2 - 11 = -49 - 11
\]
Simplifying both sides, we get:
\[
-3r^2 = -60
\]

Step2: Divide both sides by -3

Next, we divide both sides of the equation \( -3r^2 = -60 \) by -3 to solve for \( r^2 \).
\[
\frac{-3r^2}{-3} = \frac{-60}{-3}
\]
Simplifying both sides, we obtain:
\[
r^2 = 20
\]

Step3: Take the square root of both sides

To solve for \( r \), we take the square root of both sides of the equation \( r^2 = 20 \). Remember that when taking the square root, we consider both the positive and negative roots.
\[
r = \pm\sqrt{20}
\]
Simplifying \( \sqrt{20} \), we can factor 20 as \( 4 \times 5 \), so \( \sqrt{20} = \sqrt{4 \times 5} = \sqrt{4} \times \sqrt{5} = 2\sqrt{5} \). Thus,
\[
r = \pm 2\sqrt{5}
\]

Answer:

\( r = 2\sqrt{5} \) or \( r = -2\sqrt{5} \) (or approximately \( r \approx 4.47 \) or \( r \approx -4.47 \))