(x-1)*(x-1)=80

Solution for (x-1)*(x-1)=80 equation:

Simplifying
(x + -1)(x + -1) = 80

Reorder the terms:
(-1 + x)(x + -1) = 80

Reorder the terms:
(-1 + x)(-1 + x) = 80

Multiply (-1 + x) * (-1 + x)
(-1(-1 + x) + x(-1 + x)) = 80
((-1 * -1 + x * -1) + x(-1 + x)) = 80
((1 + -1x) + x(-1 + x)) = 80
(1 + -1x + (-1 * x + x * x)) = 80
(1 + -1x + (-1x + x2)) = 80

Combine like terms: -1x + -1x = -2x
(1 + -2x + x2) = 80

Solving
1 + -2x + x2 = 80

Solving for variable 'x'.

Reorder the terms:
1 + -80 + -2x + x2 = 80 + -80

Combine like terms: 1 + -80 = -79
-79 + -2x + x2 = 80 + -80

Combine like terms: 80 + -80 = 0
-79 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '79' to each side of the equation.
-79 + -2x + 79 + x2 = 0 + 79

Reorder the terms:
-79 + 79 + -2x + x2 = 0 + 79

Combine like terms: -79 + 79 = 0
0 + -2x + x2 = 0 + 79
-2x + x2 = 0 + 79

Combine like terms: 0 + 79 = 79
-2x + x2 = 79

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 79 + 1

Reorder the terms:
1 + -2x + x2 = 79 + 1

Combine like terms: 79 + 1 = 80
1 + -2x + x2 = 80

Factor a perfect square on the left side:
(x + -1)(x + -1) = 80

Calculate the square root of the right side: 8.94427191

Break this problem into two subproblems by setting 
(x + -1) equal to 8.94427191 and -8.94427191.

Subproblem 1
x + -1 = 8.94427191

Simplifying
x + -1 = 8.94427191

Reorder the terms:
-1 + x = 8.94427191

Solving
-1 + x = 8.94427191

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + x = 8.94427191 + 1

Combine like terms: -1 + 1 = 0
0 + x = 8.94427191 + 1
x = 8.94427191 + 1

Combine like terms: 8.94427191 + 1 = 9.94427191
x = 9.94427191

Simplifying
x = 9.94427191

Subproblem 2
x + -1 = -8.94427191

Simplifying
x + -1 = -8.94427191

Reorder the terms:
-1 + x = -8.94427191

Solving
-1 + x = -8.94427191

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + x = -8.94427191 + 1

Combine like terms: -1 + 1 = 0
0 + x = -8.94427191 + 1
x = -8.94427191 + 1

Combine like terms: -8.94427191 + 1 = -7.94427191
x = -7.94427191

Simplifying
x = -7.94427191

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.94427191, -7.94427191}