x^2+x=0.376

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Solution for x^2+x=0.376 equation: 


Simplifying
x2 + x = 0.376

Reorder the terms:
x + x2 = 0.376

Solving
x + x2 = 0.376

Solving for variable 'x'.

Reorder the terms:
-0.376 + x + x2 = 0.376 + -0.376

Combine like terms: 0.376 + -0.376 = 0.000
-0.376 + x + x2 = 0.000

Begin completing the square.

Move the constant term to the right:

Add '0.376' to each side of the equation.
-0.376 + x + 0.376 + x2 = 0.000 + 0.376

Reorder the terms:
-0.376 + 0.376 + x + x2 = 0.000 + 0.376

Combine like terms: -0.376 + 0.376 = 0.000
0.000 + x + x2 = 0.000 + 0.376
x + x2 = 0.000 + 0.376

Combine like terms: 0.000 + 0.376 = 0.376
x + x2 = 0.376

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 = 0.376 + 0.25

Reorder the terms:
0.25 + x + x2 = 0.376 + 0.25

Combine like terms: 0.376 + 0.25 = 0.626
0.25 + x + x2 = 0.626

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.626

Calculate the square root of the right side: 0.791201618

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.791201618 and -0.791201618.


Subproblem 1
x + 0.5 = 0.791201618

Simplifying
x + 0.5 = 0.791201618

Reorder the terms:
0.5 + x = 0.791201618

Solving
0.5 + x = 0.791201618

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 = 0.791201618 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 0.791201618 + -0.5
x = 0.791201618 + -0.5

Combine like terms: 0.791201618 + -0.5 = 0.291201618
x = 0.291201618

Simplifying
x = 0.291201618


Subproblem 2
x + 0.5 = -0.791201618

Simplifying
x + 0.5 = -0.791201618

Reorder the terms:
0.5 + x = -0.791201618

Solving
0.5 + x = -0.791201618

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 = -0.791201618 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -0.791201618 + -0.5
x = -0.791201618 + -0.5

Combine like terms: -0.791201618 + -0.5 = -1.291201618
x = -1.291201618

Simplifying
x = -1.291201618


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.291201618, -1.291201618}

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