First, take the square root of each side of the equation to solve for k while keeping the equation balanced. Remember, the square root of a number produces both a positive and negative result.
sqrt(k^2) = +-sqrt(76)
k = +-sqrt(76)
We can now simplify this using this rule for radicals:
sqrt(color(red)(a) * color(blue)(b)) = sqrt(color(red)(a)) * sqrt(color(blue)(b))
k = +-sqrt(color(red)(4) xx color(blue)(19))
k = +-sqrt(color(red)(4)) xx sqrt(color(blue)(19))
k = +-2 xx sqrt(color(blue)(19))
k = +-2sqrt(color(blue)(19))
If necessary: sqrt(19) = 4.359 rounded to the nearest thousandth
k = +-2 * 4.359
k = +-8.718 rounded to the nearest thousandth
