First, subtract #color(red)(3)# from each side of the equation to isolate the #x# term while keeping the equation balanced:
#3x^2 + 3 - color(red)(3) = 75 - color(red)(3)#
#3x^2 + 0 = 72#
#3x^2 = 72#
Next, divide each side of the equation by #color(red)(3)# to isolate #x^2# while keeping the equation balanced:
#(3x^2)/color(red)(3) = 72/color(red)(3)#
#(color(red)(cancel(color(black)(3)))x^2)/cancel(color(red)(3)) = 24#
#x^2 = 24#
Now, 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 both a negative and a positive result:
#sqrt(x^2) = +-sqrt(24)#
#x = -sqrt(4 * 6)# and #x = +sqrt(4 * 6)#
#x = -sqrt(4)sqrt(6)# and #x = sqrt(4)sqrt(6)#
#x = -2sqrt(6)# and #x = 2sqrt(6)#
Or, if a single number is needed:
#x = -2 * 2.4494# and #x = 2 * 2.4494#
#x = -4.899# and #x = 4.899# rounded to the nearest thousandth
