x^2+0.5x=0.57

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Solution for x^2+0.5x=0.57 equation: 


Simplifying
x2 + 0.5x = 0.57

Reorder the terms:
0.5x + x2 = 0.57

Solving
0.5x + x2 = 0.57

Solving for variable 'x'.

Reorder the terms:
-0.57 + 0.5x + x2 = 0.57 + -0.57

Combine like terms: 0.57 + -0.57 = 0.00
-0.57 + 0.5x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '0.57' to each side of the equation.
-0.57 + 0.5x + 0.57 + x2 = 0.00 + 0.57

Reorder the terms:
-0.57 + 0.57 + 0.5x + x2 = 0.00 + 0.57

Combine like terms: -0.57 + 0.57 = 0.00
0.00 + 0.5x + x2 = 0.00 + 0.57
0.5x + x2 = 0.00 + 0.57

Combine like terms: 0.00 + 0.57 = 0.57
0.5x + x2 = 0.57

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 0.57 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 0.57 + 0.0625

Combine like terms: 0.57 + 0.0625 = 0.6325
0.0625 + 0.5x + x2 = 0.6325

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 0.6325

Calculate the square root of the right side: 0.795298686

Break this problem into two subproblems by setting 
(x + 0.25) equal to 0.795298686 and -0.795298686.


Subproblem 1
x + 0.25 = 0.795298686

Simplifying
x + 0.25 = 0.795298686

Reorder the terms:
0.25 + x = 0.795298686

Solving
0.25 + x = 0.795298686

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 0.795298686 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 0.795298686 + -0.25
x = 0.795298686 + -0.25

Combine like terms: 0.795298686 + -0.25 = 0.545298686
x = 0.545298686

Simplifying
x = 0.545298686


Subproblem 2
x + 0.25 = -0.795298686

Simplifying
x + 0.25 = -0.795298686

Reorder the terms:
0.25 + x = -0.795298686

Solving
0.25 + x = -0.795298686

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -0.795298686 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -0.795298686 + -0.25
x = -0.795298686 + -0.25

Combine like terms: -0.795298686 + -0.25 = -1.045298686
x = -1.045298686

Simplifying
x = -1.045298686


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.545298686, -1.045298686}

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