x^2+0.579x=-0.0561

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Solution for x^2+0.579x=-0.0561 equation: 


Simplifying
x2 + 0.579x = -0.0561

Reorder the terms:
0.579x + x2 = -0.0561

Solving
0.579x + x2 = -0.0561

Solving for variable 'x'.

Reorder the terms:
0.0561 + 0.579x + x2 = -0.0561 + 0.0561

Combine like terms: -0.0561 + 0.0561 = 0.0000
0.0561 + 0.579x + x2 = 0.0000

Begin completing the square.

Move the constant term to the right:

Add '-0.0561' to each side of the equation.
0.0561 + 0.579x + -0.0561 + x2 = 0.0000 + -0.0561

Reorder the terms:
0.0561 + -0.0561 + 0.579x + x2 = 0.0000 + -0.0561

Combine like terms: 0.0561 + -0.0561 = 0.0000
0.0000 + 0.579x + x2 = 0.0000 + -0.0561
0.579x + x2 = 0.0000 + -0.0561

Combine like terms: 0.0000 + -0.0561 = -0.0561
0.579x + x2 = -0.0561

The x term is 0.579x.  Take half its coefficient (0.2895).
Square it (0.08381025) and add it to both sides.

Add '0.08381025' to each side of the equation.
0.579x + 0.08381025 + x2 = -0.0561 + 0.08381025

Reorder the terms:
0.08381025 + 0.579x + x2 = -0.0561 + 0.08381025

Combine like terms: -0.0561 + 0.08381025 = 0.02771025
0.08381025 + 0.579x + x2 = 0.02771025

Factor a perfect square on the left side:
(x + 0.2895)(x + 0.2895) = 0.02771025

Calculate the square root of the right side: 0.16646396

Break this problem into two subproblems by setting 
(x + 0.2895) equal to 0.16646396 and -0.16646396.


Subproblem 1
x + 0.2895 = 0.16646396

Simplifying
x + 0.2895 = 0.16646396

Reorder the terms:
0.2895 + x = 0.16646396

Solving
0.2895 + x = 0.16646396

Solving for variable 'x'.

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

Add '-0.2895' to each side of the equation.
0.2895 + -0.2895 + x = 0.16646396 + -0.2895

Combine like terms: 0.2895 + -0.2895 = 0.0000
0.0000 + x = 0.16646396 + -0.2895
x = 0.16646396 + -0.2895

Combine like terms: 0.16646396 + -0.2895 = -0.12303604
x = -0.12303604

Simplifying
x = -0.12303604


Subproblem 2
x + 0.2895 = -0.16646396

Simplifying
x + 0.2895 = -0.16646396

Reorder the terms:
0.2895 + x = -0.16646396

Solving
0.2895 + x = -0.16646396

Solving for variable 'x'.

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

Add '-0.2895' to each side of the equation.
0.2895 + -0.2895 + x = -0.16646396 + -0.2895

Combine like terms: 0.2895 + -0.2895 = 0.0000
0.0000 + x = -0.16646396 + -0.2895
x = -0.16646396 + -0.2895

Combine like terms: -0.16646396 + -0.2895 = -0.45596396
x = -0.45596396

Simplifying
x = -0.45596396


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.12303604, -0.45596396}

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