x^2-0.8=-0.6x

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Solution for x^2-0.8=-0.6x equation: 


Simplifying
x2 + -0.8 = -0.6x

Reorder the terms:
-0.8 + x2 = -0.6x

Solving
-0.8 + x2 = -0.6x

Solving for variable 'x'.

Reorder the terms:
-0.8 + 0.6x + x2 = -0.6x + 0.6x

Combine like terms: -0.6x + 0.6x = 0.0
-0.8 + 0.6x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '0.8' to each side of the equation.
-0.8 + 0.6x + 0.8 + x2 = 0.0 + 0.8

Reorder the terms:
-0.8 + 0.8 + 0.6x + x2 = 0.0 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + 0.6x + x2 = 0.0 + 0.8
0.6x + x2 = 0.0 + 0.8

Combine like terms: 0.0 + 0.8 = 0.8
0.6x + x2 = 0.8

The x term is 0.6x.  Take half its coefficient (0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
0.6x + 0.09 + x2 = 0.8 + 0.09

Reorder the terms:
0.09 + 0.6x + x2 = 0.8 + 0.09

Combine like terms: 0.8 + 0.09 = 0.89
0.09 + 0.6x + x2 = 0.89

Factor a perfect square on the left side:
(x + 0.3)(x + 0.3) = 0.89

Calculate the square root of the right side: 0.943398113

Break this problem into two subproblems by setting 
(x + 0.3) equal to 0.943398113 and -0.943398113.


Subproblem 1
x + 0.3 = 0.943398113

Simplifying
x + 0.3 = 0.943398113

Reorder the terms:
0.3 + x = 0.943398113

Solving
0.3 + x = 0.943398113

Solving for variable 'x'.

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

Add '-0.3' to each side of the equation.
0.3 + -0.3 + x = 0.943398113 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + x = 0.943398113 + -0.3
x = 0.943398113 + -0.3

Combine like terms: 0.943398113 + -0.3 = 0.643398113
x = 0.643398113

Simplifying
x = 0.643398113


Subproblem 2
x + 0.3 = -0.943398113

Simplifying
x + 0.3 = -0.943398113

Reorder the terms:
0.3 + x = -0.943398113

Solving
0.3 + x = -0.943398113

Solving for variable 'x'.

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

Add '-0.3' to each side of the equation.
0.3 + -0.3 + x = -0.943398113 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + x = -0.943398113 + -0.3
x = -0.943398113 + -0.3

Combine like terms: -0.943398113 + -0.3 = -1.243398113
x = -1.243398113

Simplifying
x = -1.243398113


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.643398113, -1.243398113}

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