Verified answer

x - 2√x = 8

x - 8 = 2√x

(x-8)^2 = 4x

x^2 - 16x +64 = 4x

x^2 -20x + 64 = 0

(x - 16 ) (x - 4) = 0

x = 16 or 4

Square both sides

X^2 -4x= 16

X^2-4x - 16= 0

Then use the quadratic formula

x - 2 sqrt(x) = 8

square both sides

x^2 - 4x = 64

move everything to one side

x^2 - 4x - 64 = 0

use the quadratic formula

example: x = ( -b +/- sqrt(b^2 - 4ac) ) / (2a)

x^2 - 4x - 64 = 0

a b c

a=1

b=-4

c=-64

plug into quadratic formula

( -(-4) +/- sqrt( (-4)^2 - 4(1)(-64) ) )/ ( 2(1) )

solve

( 4 +/- sqrt(16+256) )/ 2

x1=10.25

x2=-6.25