x^2+1.3x+0.4=0

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Solution for x^2+1.3x+0.4=0 equation: 


Simplifying
x2 + 1.3x + 0.4 = 0

Reorder the terms:
0.4 + 1.3x + x2 = 0

Solving
0.4 + 1.3x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.4' to each side of the equation.
0.4 + 1.3x + -0.4 + x2 = 0 + -0.4

Reorder the terms:
0.4 + -0.4 + 1.3x + x2 = 0 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + 1.3x + x2 = 0 + -0.4
1.3x + x2 = 0 + -0.4

Combine like terms: 0 + -0.4 = -0.4
1.3x + x2 = -0.4

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 = -0.4 + 0.4225

Reorder the terms:
0.4225 + 1.3x + x2 = -0.4 + 0.4225

Combine like terms: -0.4 + 0.4225 = 0.0225
0.4225 + 1.3x + x2 = 0.0225

Factor a perfect square on the left side:
(x + 0.65)(x + 0.65) = 0.0225

Calculate the square root of the right side: 0.15

Break this problem into two subproblems by setting 
(x + 0.65) equal to 0.15 and -0.15.


Subproblem 1
x + 0.65 = 0.15

Simplifying
x + 0.65 = 0.15

Reorder the terms:
0.65 + x = 0.15

Solving
0.65 + x = 0.15

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 = 0.15 + -0.65

Combine like terms: 0.65 + -0.65 = 0.00
0.00 + x = 0.15 + -0.65
x = 0.15 + -0.65

Combine like terms: 0.15 + -0.65 = -0.5
x = -0.5

Simplifying
x = -0.5


Subproblem 2
x + 0.65 = -0.15

Simplifying
x + 0.65 = -0.15

Reorder the terms:
0.65 + x = -0.15

Solving
0.65 + x = -0.15

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 = -0.15 + -0.65

Combine like terms: 0.65 + -0.65 = 0.00
0.00 + x = -0.15 + -0.65
x = -0.15 + -0.65

Combine like terms: -0.15 + -0.65 = -0.8
x = -0.8

Simplifying
x = -0.8


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.5, -0.8}

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