x^2+x=32

Solution for x^2+x=32 equation:

Simplifying
x2 + x = 32

Reorder the terms:
x + x2 = 32

Solving
x + x2 = 32

Solving for variable 'x'.

Reorder the terms:
-32 + x + x2 = 32 + -32

Combine like terms: 32 + -32 = 0
-32 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + x + 32 + x2 = 0 + 32

Reorder the terms:
-32 + 32 + x + x2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + x + x2 = 0 + 32
x + x2 = 0 + 32

Combine like terms: 0 + 32 = 32
x + x2 = 32

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 = 32 + 0.25

Reorder the terms:
0.25 + x + x2 = 32 + 0.25

Combine like terms: 32 + 0.25 = 32.25
0.25 + x + x2 = 32.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 32.25

Calculate the square root of the right side: 5.678908346

Break this problem into two subproblems by setting 
(x + 0.5) equal to 5.678908346 and -5.678908346.

Subproblem 1
x + 0.5 = 5.678908346

Simplifying
x + 0.5 = 5.678908346

Reorder the terms:
0.5 + x = 5.678908346

Solving
0.5 + x = 5.678908346

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 = 5.678908346 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 5.678908346 + -0.5
x = 5.678908346 + -0.5

Combine like terms: 5.678908346 + -0.5 = 5.178908346
x = 5.178908346

Simplifying
x = 5.178908346

Subproblem 2
x + 0.5 = -5.678908346

Simplifying
x + 0.5 = -5.678908346

Reorder the terms:
0.5 + x = -5.678908346

Solving
0.5 + x = -5.678908346

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 = -5.678908346 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -5.678908346 + -0.5
x = -5.678908346 + -0.5

Combine like terms: -5.678908346 + -0.5 = -6.178908346
x = -6.178908346

Simplifying
x = -6.178908346

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.178908346, -6.178908346}