2x^2+x=0.5

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Solution for 2x^2+x=0.5 equation: 


Simplifying
2x2 + x = 0.5

Reorder the terms:
x + 2x2 = 0.5

Solving
x + 2x2 = 0.5

Solving for variable 'x'.

Reorder the terms:
-0.5 + x + 2x2 = 0.5 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
-0.5 + x + 2x2 = 0.0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-0.25 + 0.5x + x2 = 0.0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + 0.5x + 0.25 + x2 = 0.0 + 0.25

Reorder the terms:
-0.25 + 0.25 + 0.5x + x2 = 0.0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + 0.5x + x2 = 0.0 + 0.25
0.5x + x2 = 0.0 + 0.25

Combine like terms: 0.0 + 0.25 = 0.25
0.5x + x2 = 0.25

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.
0.5x + 0.25 + x2 = 0.25 + 0.25

Reorder the terms:
0.25 + 0.5x + x2 = 0.25 + 0.25

Combine like terms: 0.25 + 0.25 = 0.5
0.25 + 0.5x + x2 = 0.5

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

Calculate the square root of the right side: 0.707106781

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.707106781 and -0.707106781.


Subproblem 1
x + 0.5 = 0.707106781

Simplifying
x + 0.5 = 0.707106781

Reorder the terms:
0.5 + x = 0.707106781

Solving
0.5 + x = 0.707106781

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 = 0.707106781 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 0.707106781 + -0.5
x = 0.707106781 + -0.5

Combine like terms: 0.707106781 + -0.5 = 0.207106781
x = 0.207106781

Simplifying
x = 0.207106781


Subproblem 2
x + 0.5 = -0.707106781

Simplifying
x + 0.5 = -0.707106781

Reorder the terms:
0.5 + x = -0.707106781

Solving
0.5 + x = -0.707106781

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 = -0.707106781 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -0.707106781 + -0.5
x = -0.707106781 + -0.5

Combine like terms: -0.707106781 + -0.5 = -1.207106781
x = -1.207106781

Simplifying
x = -1.207106781


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.207106781, -1.207106781}

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