First, subtract color(red)(1)1 from each side of the equation to isolate the x^2x2 term while keeping the equation balanced:
4x^2 + 1 - color(red)(1) = a - color(red)(1)4x2+1−1=a−1
4x^2 + 0 = a - 14x2+0=a−1
4x^2 = a - 14x2=a−1
Next, divide each side of the equation by color(red)(4)4 to isolate x^2x2 while keeping the equation balanced:
(4x^2)/color(red)(4) = (a - 1)/color(red)(4)4x24=a−14
(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.
