X^2+X=0.31

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Solution for X^2+X=0.31 equation: 


Simplifying
X2 + X = 0.31

Reorder the terms:
X + X2 = 0.31

Solving
X + X2 = 0.31

Solving for variable 'X'.

Reorder the terms:
-0.31 + X + X2 = 0.31 + -0.31

Combine like terms: 0.31 + -0.31 = 0.00
-0.31 + X + X2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '0.31' to each side of the equation.
-0.31 + X + 0.31 + X2 = 0.00 + 0.31

Reorder the terms:
-0.31 + 0.31 + X + X2 = 0.00 + 0.31

Combine like terms: -0.31 + 0.31 = 0.00
0.00 + X + X2 = 0.00 + 0.31
X + X2 = 0.00 + 0.31

Combine like terms: 0.00 + 0.31 = 0.31
X + X2 = 0.31

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 = 0.31 + 0.25

Reorder the terms:
0.25 + X + X2 = 0.31 + 0.25

Combine like terms: 0.31 + 0.25 = 0.56
0.25 + X + X2 = 0.56

Factor a perfect square on the left side:
(X + 0.5)(X + 0.5) = 0.56

Calculate the square root of the right side: 0.748331477

Break this problem into two subproblems by setting 
(X + 0.5) equal to 0.748331477 and -0.748331477.


Subproblem 1
X + 0.5 = 0.748331477

Simplifying
X + 0.5 = 0.748331477

Reorder the terms:
0.5 + X = 0.748331477

Solving
0.5 + X = 0.748331477

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 = 0.748331477 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + X = 0.748331477 + -0.5
X = 0.748331477 + -0.5

Combine like terms: 0.748331477 + -0.5 = 0.248331477
X = 0.248331477

Simplifying
X = 0.248331477


Subproblem 2
X + 0.5 = -0.748331477

Simplifying
X + 0.5 = -0.748331477

Reorder the terms:
0.5 + X = -0.748331477

Solving
0.5 + X = -0.748331477

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 = -0.748331477 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + X = -0.748331477 + -0.5
X = -0.748331477 + -0.5

Combine like terms: -0.748331477 + -0.5 = -1.248331477
X = -1.248331477

Simplifying
X = -1.248331477


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {0.248331477, -1.248331477}

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