x^2-2x-90=0

Solution for x^2-2x-90=0 equation:

Simplifying
x2 + -2x + -90 = 0

Reorder the terms:
-90 + -2x + x2 = 0

Solving
-90 + -2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + -2x + 90 + x2 = 0 + 90

Reorder the terms:
-90 + 90 + -2x + x2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + -2x + x2 = 0 + 90
-2x + x2 = 0 + 90

Combine like terms: 0 + 90 = 90
-2x + x2 = 90

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 = 90 + 1

Reorder the terms:
1 + -2x + x2 = 90 + 1

Combine like terms: 90 + 1 = 91
1 + -2x + x2 = 91

Factor a perfect square on the left side:
(x + -1)(x + -1) = 91

Calculate the square root of the right side: 9.539392014

Break this problem into two subproblems by setting 
(x + -1) equal to 9.539392014 and -9.539392014.

Subproblem 1
x + -1 = 9.539392014

Simplifying
x + -1 = 9.539392014

Reorder the terms:
-1 + x = 9.539392014

Solving
-1 + x = 9.539392014

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 = 9.539392014 + 1

Combine like terms: -1 + 1 = 0
0 + x = 9.539392014 + 1
x = 9.539392014 + 1

Combine like terms: 9.539392014 + 1 = 10.539392014
x = 10.539392014

Simplifying
x = 10.539392014

Subproblem 2
x + -1 = -9.539392014

Simplifying
x + -1 = -9.539392014

Reorder the terms:
-1 + x = -9.539392014

Solving
-1 + x = -9.539392014

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 = -9.539392014 + 1

Combine like terms: -1 + 1 = 0
0 + x = -9.539392014 + 1
x = -9.539392014 + 1

Combine like terms: -9.539392014 + 1 = -8.539392014
x = -8.539392014

Simplifying
x = -8.539392014

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.539392014, -8.539392014}