x^2+x=1764

Solution for x^2+x=1764 equation:

Simplifying
x2 + x = 1764

Reorder the terms:
x + x2 = 1764

Solving
x + x2 = 1764

Solving for variable 'x'.

Reorder the terms:
-1764 + x + x2 = 1764 + -1764

Combine like terms: 1764 + -1764 = 0
-1764 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1764' to each side of the equation.
-1764 + x + 1764 + x2 = 0 + 1764

Reorder the terms:
-1764 + 1764 + x + x2 = 0 + 1764

Combine like terms: -1764 + 1764 = 0
0 + x + x2 = 0 + 1764
x + x2 = 0 + 1764

Combine like terms: 0 + 1764 = 1764
x + x2 = 1764

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 = 1764 + 0.25

Reorder the terms:
0.25 + x + x2 = 1764 + 0.25

Combine like terms: 1764 + 0.25 = 1764.25
0.25 + x + x2 = 1764.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 1764.25

Calculate the square root of the right side: 42.002976085

Break this problem into two subproblems by setting 
(x + 0.5) equal to 42.002976085 and -42.002976085.

Subproblem 1
x + 0.5 = 42.002976085

Simplifying
x + 0.5 = 42.002976085

Reorder the terms:
0.5 + x = 42.002976085

Solving
0.5 + x = 42.002976085

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 = 42.002976085 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 42.002976085 + -0.5
x = 42.002976085 + -0.5

Combine like terms: 42.002976085 + -0.5 = 41.502976085
x = 41.502976085

Simplifying
x = 41.502976085

Subproblem 2
x + 0.5 = -42.002976085

Simplifying
x + 0.5 = -42.002976085

Reorder the terms:
0.5 + x = -42.002976085

Solving
0.5 + x = -42.002976085

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 = -42.002976085 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -42.002976085 + -0.5
x = -42.002976085 + -0.5

Combine like terms: -42.002976085 + -0.5 = -42.502976085
x = -42.502976085

Simplifying
x = -42.502976085

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {41.502976085, -42.502976085}