First, add #color(red)(7)# to each side of the equation to isolate the #x# term while keeping the equation balanced:
#6x^2 - 7 + color(red)(7) = 257 + color(red)(7)#
#6x^2 - 0 = 264#
#6x^2 = 264#
Next, divide each side of the equation by #color(red)(6)# to isolate #x^2# while keeping the equation balanced:
#(6x^2)/color(red)(6) = 264/color(red)(6)#
#(color(red)(cancel(color(black)(6)))x^2)/cancel(color(red)(6)) = 44#
#x^2 = 44#
Next, take the square root of each side of the equation to solve for #x# while keeping the equation balanced. Remember the square root of a number produces a positive and negative result:
#sqrt(x^2) = sqrt(44)#
#x = sqrt(4 xx 11)#
#x = +-2sqrt(11)#
Or
#x = +-6.633# rounded to the nearest thousandth.
