x^2-2x-37=0

Solution for x^2-2x-37=0 equation:

Simplifying
x2 + -2x + -37 = 0

Reorder the terms:
-37 + -2x + x2 = 0

Solving
-37 + -2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '37' to each side of the equation.
-37 + -2x + 37 + x2 = 0 + 37

Reorder the terms:
-37 + 37 + -2x + x2 = 0 + 37

Combine like terms: -37 + 37 = 0
0 + -2x + x2 = 0 + 37
-2x + x2 = 0 + 37

Combine like terms: 0 + 37 = 37
-2x + x2 = 37

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 = 37 + 1

Reorder the terms:
1 + -2x + x2 = 37 + 1

Combine like terms: 37 + 1 = 38
1 + -2x + x2 = 38

Factor a perfect square on the left side:
(x + -1)(x + -1) = 38

Calculate the square root of the right side: 6.164414003

Break this problem into two subproblems by setting 
(x + -1) equal to 6.164414003 and -6.164414003.

Subproblem 1
x + -1 = 6.164414003

Simplifying
x + -1 = 6.164414003

Reorder the terms:
-1 + x = 6.164414003

Solving
-1 + x = 6.164414003

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 = 6.164414003 + 1

Combine like terms: -1 + 1 = 0
0 + x = 6.164414003 + 1
x = 6.164414003 + 1

Combine like terms: 6.164414003 + 1 = 7.164414003
x = 7.164414003

Simplifying
x = 7.164414003

Subproblem 2
x + -1 = -6.164414003

Simplifying
x + -1 = -6.164414003

Reorder the terms:
-1 + x = -6.164414003

Solving
-1 + x = -6.164414003

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 = -6.164414003 + 1

Combine like terms: -1 + 1 = 0
0 + x = -6.164414003 + 1
x = -6.164414003 + 1

Combine like terms: -6.164414003 + 1 = -5.164414003
x = -5.164414003

Simplifying
x = -5.164414003

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.164414003, -5.164414003}