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 = 0.8
x = 0.8

Simplifying
x = 0.8


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 = 0.5
x = 0.5

Simplifying
x = 0.5


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

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