First, subtract #color(red)(4)# from each side of the equation to isolate the #m# term while keeping the equation balanced:
#6m^2 + 4 - color(red)(4) = 292 - color(red)(4)#
#6m^2 + 0 = 288#
#6m^2 = 288#
Next, divide each side of the equation by #color(red)(6)# to isolate the #m^2# term while keeping the equation balanced:
#(6m^2)/color(red)(6) = 288/color(red)(6)#
#(color(red)(cancel(color(black)(6)))m^2)/cancel(color(red)(6)) = 48#
#m^2 = 48#
Next, take the square root of each side of the equation to solve for #m# while keeping the equation balanced. Remember, the square root of a number produces a positive and negative result:
#sqrt(m^2) = sqrt(48)#
#m = sqrt(16 * 3)#
#m = sqrt(16) * sqrt(3)#
#m = +-4sqrt(3)#
Or
#m = +-6.928# rounded to the nearest thousandth.
