First, subtract #color(red)(3)# from each side of the equation to isolate the #a# term while keeping the equation balanced:
#a^2 + 3 - color(red)(3) = 51 - color(red)(3)#
#a^2 + 0 = 48#
#a^2 = 48#
Now, take the square root of each side of the equation to solve for #a# while keeping the equation balanced. Remember, the square root of a number produces a positive and negative result:
#sqrt(a^2) = +-sqrt(48)#
#a = +-sqrt(48)#
We can rewrite the radical and simplify using this rule for radicals:
#sqrt(color(red)(a) * color(blue)(b)) = sqrt(color(red)(a)) * sqrt(color(blue)(b))#
#a = +-sqrt(16 * 3)#
#a = +-sqrt(16) * sqrt(3)#
#a = +-4sqrt(12)#
If necessary, the numerical answer is:
#a = +-6.928# rounded to the nearest thousandth
