k^2-2k-90=0

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

Simplifying
k2 + -2k + -90 = 0

Reorder the terms:
-90 + -2k + k2 = 0

Solving
-90 + -2k + k2 = 0

Solving for variable 'k'.

Begin completing the square.

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + -2k + 90 + k2 = 0 + 90

Reorder the terms:
-90 + 90 + -2k + k2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + -2k + k2 = 0 + 90
-2k + k2 = 0 + 90

Combine like terms: 0 + 90 = 90
-2k + k2 = 90

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

Add '1' to each side of the equation.
-2k + 1 + k2 = 90 + 1

Reorder the terms:
1 + -2k + k2 = 90 + 1

Combine like terms: 90 + 1 = 91
1 + -2k + k2 = 91

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

Calculate the square root of the right side: 9.539392014

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

Subproblem 1
k + -1 = 9.539392014

Simplifying
k + -1 = 9.539392014

Reorder the terms:
-1 + k = 9.539392014

Solving
-1 + k = 9.539392014

Solving for variable 'k'.

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

Add '1' to each side of the equation.
-1 + 1 + k = 9.539392014 + 1

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

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

Simplifying
k = 10.539392014

Subproblem 2
k + -1 = -9.539392014

Simplifying
k + -1 = -9.539392014

Reorder the terms:
-1 + k = -9.539392014

Solving
-1 + k = -9.539392014

Solving for variable 'k'.

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

Add '1' to each side of the equation.
-1 + 1 + k = -9.539392014 + 1

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

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

Simplifying
k = -8.539392014

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