Could you please explain how are these the answers?Its about solving polynomials?

Question

^=squared 1) 1+x^=2X
2) 4t^=8t
3) 2y^+12y= -10
4)(X-7)(X+1)= -16
5)81x^ -5=20
The book says the answer to these five are
1)1 2)0,2 3)-5,-1 4)3 5)-5over9

Answer 1

1) 1+x^=2X
x^2 -2x+1 =0
then (x-1)^2 = 0
x = 1

2) 4t^=8t
4t^2-8t = 0
t(4t-8)=0
t = 0, 2

3) 2y^+12y= -10
y^2 + 6y + 5 = 0
(y+1)(y+5)=0
y=-1, -5

4)(X-7)(X+1)= -16
Expand
x^2 -6x -7 +16=0
x^2 -6x + 9 =0
(x-3)^2=0
x = 3

5)81x^ -5=20
81x^2 = 25
x = sqrt(25/81)
= +5/9 or -5/9

Answer 2

1)1 + x^2 = 2x
x^2 - 2x + 1 = 0
(x - 1)(x - 1) = 0
x = (1,2)

2) 4t^2 = 8t
4t^2 - 8t = 0
t^2 - 2t = 0
t(t - 2) = 0
t = (0,2)

3) 2y^2 + 12y = -10
y^2 + 6y = -5
y^2 + 6y + 5 = 0
(y + 1)(y + 5) = 0
y = (-1,-5)

4) (x - 7)(x + 1) = - 16
x^2 - 6x - 7 = - 16
x^2 - 6x + 9 = 0
(x - 3)^2 = 0
x = 3

5) 81x^2 - 5 = 20
81x^2 = 25
x^2 = 25/81
x = (-5/9)(5/9)