x^2+x-1040=0

Solution for x^2+x-1040=0 equation:

Simplifying
x2 + x + -1040 = 0

Reorder the terms:
-1040 + x + x2 = 0

Solving
-1040 + x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1040' to each side of the equation.
-1040 + x + 1040 + x2 = 0 + 1040

Reorder the terms:
-1040 + 1040 + x + x2 = 0 + 1040

Combine like terms: -1040 + 1040 = 0
0 + x + x2 = 0 + 1040
x + x2 = 0 + 1040

Combine like terms: 0 + 1040 = 1040
x + x2 = 1040

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 1040 + 0.25

Reorder the terms:
0.25 + x + x2 = 1040 + 0.25

Combine like terms: 1040 + 0.25 = 1040.25
0.25 + x + x2 = 1040.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 1040.25

Calculate the square root of the right side: 32.252906846

Break this problem into two subproblems by setting 
(x + 0.5) equal to 32.252906846 and -32.252906846.

Subproblem 1
x + 0.5 = 32.252906846

Simplifying
x + 0.5 = 32.252906846

Reorder the terms:
0.5 + x = 32.252906846

Solving
0.5 + x = 32.252906846

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 32.252906846 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 32.252906846 + -0.5
x = 32.252906846 + -0.5

Combine like terms: 32.252906846 + -0.5 = 31.752906846
x = 31.752906846

Simplifying
x = 31.752906846

Subproblem 2
x + 0.5 = -32.252906846

Simplifying
x + 0.5 = -32.252906846

Reorder the terms:
0.5 + x = -32.252906846

Solving
0.5 + x = -32.252906846

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -32.252906846 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -32.252906846 + -0.5
x = -32.252906846 + -0.5

Combine like terms: -32.252906846 + -0.5 = -32.752906846
x = -32.752906846

Simplifying
x = -32.752906846

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {31.752906846, -32.752906846}