x^2+1.3x+.2=0

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Solution for x^2+1.3x+.2=0 equation: 


Simplifying
x2 + 1.3x + 0.2 = 0

Reorder the terms:
0.2 + 1.3x + x2 = 0

Solving
0.2 + 1.3x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + 1.3x + -0.2 + x2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + 1.3x + x2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + 1.3x + x2 = 0 + -0.2
1.3x + x2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
1.3x + x2 = -0.2

The x term is 1.3x.  Take half its coefficient (0.65).
Square it (0.4225) and add it to both sides.

Add '0.4225' to each side of the equation.
1.3x + 0.4225 + x2 = -0.2 + 0.4225

Reorder the terms:
0.4225 + 1.3x + x2 = -0.2 + 0.4225

Combine like terms: -0.2 + 0.4225 = 0.2225
0.4225 + 1.3x + x2 = 0.2225

Factor a perfect square on the left side:
(x + 0.65)(x + 0.65) = 0.2225

Calculate the square root of the right side: 0.471699057

Break this problem into two subproblems by setting 
(x + 0.65) equal to 0.471699057 and -0.471699057.


Subproblem 1
x + 0.65 = 0.471699057

Simplifying
x + 0.65 = 0.471699057

Reorder the terms:
0.65 + x = 0.471699057

Solving
0.65 + x = 0.471699057

Solving for variable 'x'.

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

Add '-0.65' to each side of the equation.
0.65 + -0.65 + x = 0.471699057 + -0.65

Combine like terms: 0.65 + -0.65 = 0.00
0.00 + x = 0.471699057 + -0.65
x = 0.471699057 + -0.65

Combine like terms: 0.471699057 + -0.65 = -0.178300943
x = -0.178300943

Simplifying
x = -0.178300943


Subproblem 2
x + 0.65 = -0.471699057

Simplifying
x + 0.65 = -0.471699057

Reorder the terms:
0.65 + x = -0.471699057

Solving
0.65 + x = -0.471699057

Solving for variable 'x'.

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

Add '-0.65' to each side of the equation.
0.65 + -0.65 + x = -0.471699057 + -0.65

Combine like terms: 0.65 + -0.65 = 0.00
0.00 + x = -0.471699057 + -0.65
x = -0.471699057 + -0.65

Combine like terms: -0.471699057 + -0.65 = -1.121699057
x = -1.121699057

Simplifying
x = -1.121699057


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.178300943, -1.121699057}

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