Question

2v² - 47 = 61

Explanation:

Step1: Add 47 to both sides

To isolate the term with \( v^2 \), we add 47 to both sides of the equation \( 2v^2 - 47 = 61 \). This gives us \( 2v^2 - 47 + 47 = 61 + 47 \), which simplifies to \( 2v^2 = 108 \).

Step2: Divide both sides by 2

Next, we divide both sides of the equation \( 2v^2 = 108 \) by 2 to solve for \( v^2 \). So, \( \frac{2v^2}{2} = \frac{108}{2} \), which simplifies to \( v^2 = 54 \).

Step3: Take square root of both sides

To find the value of \( v \), we take the square root of both sides of the equation \( v^2 = 54 \). Remembering that the square root of a number has two solutions (positive and negative), we get \( v = \pm\sqrt{54} \). Simplifying \( \sqrt{54} \), we can factor 54 as \( 9\times6 \), so \( \sqrt{54} = \sqrt{9\times6} = 3\sqrt{6} \). Thus, \( v = \pm 3\sqrt{6} \).

Answer:

\( v = 3\sqrt{6} \) or \( v = -3\sqrt{6} \) (or approximately \( v \approx 7.35 \) or \( v \approx -7.35 \))