0.6=0.4x+x^2

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Solution for 0.6=0.4x+x^2 equation: 


Simplifying
0.6 = 0.4x + x2

Solving
0.6 = 0.4x + x2

Solving for variable 'x'.

Reorder the terms:
0.6 + -0.4x + -1x2 = 0.4x + -0.4x + x2 + -1x2

Combine like terms: 0.4x + -0.4x = 0.0
0.6 + -0.4x + -1x2 = 0.0 + x2 + -1x2
0.6 + -0.4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
0.6 + -0.4x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-0.6 + 0.4x + x2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + 0.4x + 0.6 + x2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + 0.4x + x2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + 0.4x + x2 = 0 + 0.6
0.4x + x2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
0.4x + x2 = 0.6

The x term is 0.4x.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4x + 0.04 + x2 = 0.6 + 0.04

Reorder the terms:
0.04 + 0.4x + x2 = 0.6 + 0.04

Combine like terms: 0.6 + 0.04 = 0.64
0.04 + 0.4x + x2 = 0.64

Factor a perfect square on the left side:
(x + 0.2)(x + 0.2) = 0.64

Calculate the square root of the right side: 0.8

Break this problem into two subproblems by setting 
(x + 0.2) equal to 0.8 and -0.8.


Subproblem 1
x + 0.2 = 0.8

Simplifying
x + 0.2 = 0.8

Reorder the terms:
0.2 + x = 0.8

Solving
0.2 + x = 0.8

Solving for variable 'x'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + x = 0.8 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + x = 0.8 + -0.2
x = 0.8 + -0.2

Combine like terms: 0.8 + -0.2 = 0.6
x = 0.6

Simplifying
x = 0.6


Subproblem 2
x + 0.2 = -0.8

Simplifying
x + 0.2 = -0.8

Reorder the terms:
0.2 + x = -0.8

Solving
0.2 + x = -0.8

Solving for variable 'x'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + x = -0.8 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + x = -0.8 + -0.2
x = -0.8 + -0.2

Combine like terms: -0.8 + -0.2 = -1
x = -1

Simplifying
x = -1


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.6, -1}

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