First, subtract #color(red)(1)# from each side of the equation to isolate the #x^2# term while keeping the equation balanced:

#4x^2 + 1 - color(red)(1) = a - color(red)(1)#

#4x^2 + 0 = a - 1#

#4x^2 = a - 1#

Next, divide each side of the equation by #color(red)(4)# to isolate #x^2# while keeping the equation balanced:

#(4x^2)/color(red)(4) = (a - 1)/color(red)(4)#

#(color(red)(cancel(color(black)(4)))x^2)/cancel(color(red)(4)) = (a - 1)/4#

#x^2 = (a - 1)/4#

Now, take the square root of each side of the equation to solve for #x#. However, remember when taking the square root of a number there will be a negative and positive result:

#sqrt(x^2) = +-sqrt((a - 1)/4)#

#x = +-sqrt(a - 1)/sqrt(4)#

#x = +-sqrt(a - 1)/2# where #a - 1 >= 0# or #a >= 1#

Because we cannot take the square root of a negative number.