First, subtract #color(red)(1)# from each side of the equation to isolate the radical while keeping the equation balanced:
#sqrt(8x) + 1 - color(red)(1) = 65 - color(red)(1)#
#sqrt(8x) + 0 = 64#
#sqrt(8x) = 64#
Next, square each side of the equation to remove the radical while keeping the equation balanced:
#(sqrt(8x))^2 = 64^2#
#8x = 4096#
Now, divide each side of the equation by #color(red)(8)# to solve for #x# while keeping the equation balanced:
#(8x)/color(red)(8) = 4096/color(red)(8)#
#(color(red)(cancel(color(black)(8)))x)/cancel(color(red)(8)) = 512#
#x = 512#
To check the solution substitute #color(red)(512)# for #color(red)(x)# and calculate each side of the equation to ensure both sides are equal:
#sqrt(8color(red)(x)) + 1 = 65# becomes:
#sqrt(8 * color(red)(512)) + 1 = 65#
#sqrt(4096) + 1 = 65#
#64 + 1 = 65#
#65 + 65#
Both sides of the equation are equal therefore the solution is valid.
