how to solve for x? x^2-2x-8=4^2?

complete the equation in one side

x^2 -2x -8 - 16 =0

x^2 -2x -24 = 0
(x-6)(x+4)=0
x=6 or x =-4

x² - 2x - 8 = 4²
x² - x = 16 + 8 + (- 1)²
x² - x = 24 + 1
(x - 1)² = 25
x - 1 = 5

x = 5 + 1, x = 6
x = - 5 + 1, x = - 4

Answer: x = 6, - 4

Proof (x = 6):
6² - 2(6) - 8 = 4²
36 - 12 - 8 = 16
16 = 16

Proof (x = - 4):
(- 4)² - 2(- 4) - 8 = 4²
16 + 8 - 8 = 16
16 = 16

x^2 - 2x - 8 = 4^2
x^2 - 2x - 8 - 16 = 0
x^2 - 2x - 24 = 0
x^2 + 4x - 6x - 24 = 0
(x^2 + 4x) - (6x + 24) = 0
x(x + 4) - 6(x + 4) = 0
(x + 4)(x - 6) = 0

x + 4 = 0
x = -4

x - 6 = 0
x = 6

∴ x = -4, 6

by taking factors you can get the answer -4 or 6. Let me show you another way.
you should know x^2-2x+1 = (x-1)^2.
ok, as x2-2x-8=16
x2-2x=24
x2-2x+1=25 ( I have added +1 for both side)
as x2-2x+1= (x-1)2
(x-1)2= 25
getting the sqrt of both side, x-1= +5 or -5
so, x= 6 or x= -4.

x ² - 2 x - 8 = 16

x ² - 2 x - 24 = 0

( x - 6 ) ( x + 4 ) = 0

x = 6 , x = - 4

x^2-2x-8=4^2
x^2-2x-8=16
subtract 16 to both sides.
x^2-2x-24=0
(x+4)(x-6)=0
x+4=0 or x-6=0
x=-4 or x=6

x= -4 and 6