Verified answer

1)

(x+9)²-x(x+8)=1

x²+18x+81-x²-8x=1

10x+81=1

10x= -80

x= -8

2)

(x-11)²=(x-7)(x-9)

x²-22x+121=x^2-7x-9x+63

-22x+121= -16x+63

-6x= -58

x= 58/6

x=9 ²/₃

3)

(x-4)(x+4)-(x+6)²= -16

x²-16-(x²+12x+36)= -16

x²-16-x²-12x-36= -16

-12x=36

x= -3

4)

(1-3x)²-x(9x-2)=2

1-6x+9x²-9x²+2x=2

-4x = 1

x= -¹/₄