x^2-0.6=-0.6x

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


Simplifying
x2 + -0.6 = -0.6x

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

Solving
-0.6 + x2 = -0.6x

Solving for variable 'x'.

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

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

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = 0.6 + 0.09

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

Combine like terms: 0.6 + 0.09 = 0.69
0.09 + 0.6x + x2 = 0.69

Factor a perfect square on the left side:
(x + 0.3)(x + 0.3) = 0.69

Calculate the square root of the right side: 0.830662386

Break this problem into two subproblems by setting 
(x + 0.3) equal to 0.830662386 and -0.830662386.


Subproblem 1
x + 0.3 = 0.830662386

Simplifying
x + 0.3 = 0.830662386

Reorder the terms:
0.3 + x = 0.830662386

Solving
0.3 + x = 0.830662386

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 = 0.830662386 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + x = 0.830662386 + -0.3
x = 0.830662386 + -0.3

Combine like terms: 0.830662386 + -0.3 = 0.530662386
x = 0.530662386

Simplifying
x = 0.530662386


Subproblem 2
x + 0.3 = -0.830662386

Simplifying
x + 0.3 = -0.830662386

Reorder the terms:
0.3 + x = -0.830662386

Solving
0.3 + x = -0.830662386

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 = -0.830662386 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + x = -0.830662386 + -0.3
x = -0.830662386 + -0.3

Combine like terms: -0.830662386 + -0.3 = -1.130662386
x = -1.130662386

Simplifying
x = -1.130662386


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.530662386, -1.130662386}

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