0.18x^2+0.82x-0.255=0

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Solution for 0.18x^2+0.82x-0.255=0 equation: 


Simplifying
0.18x2 + 0.82x + -0.255 = 0

Reorder the terms:
-0.255 + 0.82x + 0.18x2 = 0

Solving
-0.255 + 0.82x + 0.18x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.18'.
-1.416666667 + 4.555555556x + x2 = 0

Move the constant term to the right:

Add '1.416666667' to each side of the equation.
-1.416666667 + 4.555555556x + 1.416666667 + x2 = 0 + 1.416666667

Reorder the terms:
-1.416666667 + 1.416666667 + 4.555555556x + x2 = 0 + 1.416666667

Combine like terms: -1.416666667 + 1.416666667 = 0.000000000
0.000000000 + 4.555555556x + x2 = 0 + 1.416666667
4.555555556x + x2 = 0 + 1.416666667

Combine like terms: 0 + 1.416666667 = 1.416666667
4.555555556x + x2 = 1.416666667

The x term is 4.555555556x.  Take half its coefficient (2.277777778).
Square it (5.188271606) and add it to both sides.

Add '5.188271606' to each side of the equation.
4.555555556x + 5.188271606 + x2 = 1.416666667 + 5.188271606

Reorder the terms:
5.188271606 + 4.555555556x + x2 = 1.416666667 + 5.188271606

Combine like terms: 1.416666667 + 5.188271606 = 6.604938273
5.188271606 + 4.555555556x + x2 = 6.604938273

Factor a perfect square on the left side:
(x + 2.277777778)(x + 2.277777778) = 6.604938273

Calculate the square root of the right side: 2.570007446

Break this problem into two subproblems by setting 
(x + 2.277777778) equal to 2.570007446 and -2.570007446.


Subproblem 1
x + 2.277777778 = 2.570007446

Simplifying
x + 2.277777778 = 2.570007446

Reorder the terms:
2.277777778 + x = 2.570007446

Solving
2.277777778 + x = 2.570007446

Solving for variable 'x'.

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

Add '-2.277777778' to each side of the equation.
2.277777778 + -2.277777778 + x = 2.570007446 + -2.277777778

Combine like terms: 2.277777778 + -2.277777778 = 0.000000000
0.000000000 + x = 2.570007446 + -2.277777778
x = 2.570007446 + -2.277777778

Combine like terms: 2.570007446 + -2.277777778 = 0.292229668
x = 0.292229668

Simplifying
x = 0.292229668


Subproblem 2
x + 2.277777778 = -2.570007446

Simplifying
x + 2.277777778 = -2.570007446

Reorder the terms:
2.277777778 + x = -2.570007446

Solving
2.277777778 + x = -2.570007446

Solving for variable 'x'.

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

Add '-2.277777778' to each side of the equation.
2.277777778 + -2.277777778 + x = -2.570007446 + -2.277777778

Combine like terms: 2.277777778 + -2.277777778 = 0.000000000
0.000000000 + x = -2.570007446 + -2.277777778
x = -2.570007446 + -2.277777778

Combine like terms: -2.570007446 + -2.277777778 = -4.847785224
x = -4.847785224

Simplifying
x = -4.847785224


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.292229668, -4.847785224}

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