Solve this equation. 16^(x^2-2*x-1)=2?

2^[4(x^2-2*x-1)] = 2
4(x^2-2x-1) = 1
(2x)^2 - 4(2x) - 5 = 0
(2x-5)(2x+1) = 0
x = 5/2, -1/2

16^(x^2-2*x-1)=2
2^4(x^2-2x-1) = 2^1
4x^2 - 8x - 4 = 1
4x^2 - 8x -5 = 0
4x^2 + 2x - 10x - 5 = 0
2x(x + 1) - 2(x+1) = 0
(2x-2)(x+1) = 0
x = 1 or -1

x ² - 2 x - 1 = 1 / 4

4 x ² - 8 x - 4 = 1

4 x ² - 8 x - 5 = 0

( 2 x - 5 ) ( 2 x + 1 ) = 0

x = 5/2 , x = - 1/2

16^(x^2 - 2x - 1) = 2
(2^4)^(x^2 - 2x - 1) = 2^1
2^[4(x^2 - 2x - 1)] = 2^1
4(x^2 - 2x - 1) = 1
4x^2 - 8x - 4 = 1
4x^2 - 8x - 4 - 1 = 0
4x^2 - 8x - 5 = 0
4x^2 + 2x - 10x - 5 = 0
(4x^2 + 2x) - (10x + 5) = 0
2x(2x + 1) - 5(2x + 1) = 0
(2x + 1)(2x - 5) = 0

2x + 1 = 0
2x = -1
x = -1/2 (-0.5)

2x - 5 = 0
2x = 5
x = 5/2 (2.5)

∴ x = -1/2 (-0.5), 5/2 (2.5)

the fourth root of 16 is 2
16^1/4 = 2

x^2 - 2x - 1 = 1/4
4x^2 - 8x - 4 - 1 = 0
4x^2 - 8x - 5 = 0
(2x + 1)(2x -5) = 0

x = -1/2 or x= 5/2

the fourth root of 16 is 2 therefore 16^1/4 = 2

next, x^2 - 2x - 1 = 1/4
4x^2 - 8x - 4 - 1 = 0
4x^2 - 8x - 5 = 0
(2x + 1)(2x -5) = 0

2x +1 = 0
2x = -1
x = -1/2

2x - 5 = 0
2x = 5
x = 5/2

answers: x = -1/2 or 5/2

1

the answer is...
heck i duno use a calculator