x^2+x=0.32746

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Solution for x^2+x=0.32746 equation: 


Simplifying
x2 + x = 0.32746

Reorder the terms:
x + x2 = 0.32746

Solving
x + x2 = 0.32746

Solving for variable 'x'.

Reorder the terms:
-0.32746 + x + x2 = 0.32746 + -0.32746

Combine like terms: 0.32746 + -0.32746 = 0.00000
-0.32746 + x + x2 = 0.00000

Begin completing the square.

Move the constant term to the right:

Add '0.32746' to each side of the equation.
-0.32746 + x + 0.32746 + x2 = 0.00000 + 0.32746

Reorder the terms:
-0.32746 + 0.32746 + x + x2 = 0.00000 + 0.32746

Combine like terms: -0.32746 + 0.32746 = 0.00000
0.00000 + x + x2 = 0.00000 + 0.32746
x + x2 = 0.00000 + 0.32746

Combine like terms: 0.00000 + 0.32746 = 0.32746
x + x2 = 0.32746

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 = 0.32746 + 0.25

Reorder the terms:
0.25 + x + x2 = 0.32746 + 0.25

Combine like terms: 0.32746 + 0.25 = 0.57746
0.25 + x + x2 = 0.57746

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.57746

Calculate the square root of the right side: 0.759907889

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.759907889 and -0.759907889.


Subproblem 1
x + 0.5 = 0.759907889

Simplifying
x + 0.5 = 0.759907889

Reorder the terms:
0.5 + x = 0.759907889

Solving
0.5 + x = 0.759907889

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 = 0.759907889 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 0.759907889 + -0.5
x = 0.759907889 + -0.5

Combine like terms: 0.759907889 + -0.5 = 0.259907889
x = 0.259907889

Simplifying
x = 0.259907889


Subproblem 2
x + 0.5 = -0.759907889

Simplifying
x + 0.5 = -0.759907889

Reorder the terms:
0.5 + x = -0.759907889

Solving
0.5 + x = -0.759907889

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 = -0.759907889 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -0.759907889 + -0.5
x = -0.759907889 + -0.5

Combine like terms: -0.759907889 + -0.5 = -1.259907889
x = -1.259907889

Simplifying
x = -1.259907889


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.259907889, -1.259907889}

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