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Simplifying
x2 = 0.6x + -0.08

Reorder the terms:
x2 = -0.08 + 0.6x

Solving
x2 = -0.08 + 0.6x

Solving for variable 'x'.

Reorder the terms:
0.08 + -0.6x + x2 = -0.08 + 0.6x + 0.08 + -0.6x

Reorder the terms:
0.08 + -0.6x + x2 = -0.08 + 0.08 + 0.6x + -0.6x

Combine like terms: -0.08 + 0.08 = 0.00
0.08 + -0.6x + x2 = 0.00 + 0.6x + -0.6x
0.08 + -0.6x + x2 = 0.6x + -0.6x

Combine like terms: 0.6x + -0.6x = 0.0
0.08 + -0.6x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '-0.08' to each side of the equation.
0.08 + -0.6x + -0.08 + x2 = 0.0 + -0.08

Reorder the terms:
0.08 + -0.08 + -0.6x + x2 = 0.0 + -0.08

Combine like terms: 0.08 + -0.08 = 0.00
0.00 + -0.6x + x2 = 0.0 + -0.08
-0.6x + x2 = 0.0 + -0.08

Combine like terms: 0.0 + -0.08 = -0.08
-0.6x + x2 = -0.08

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 = -0.08 + 0.09

Reorder the terms:
0.09 + -0.6x + x2 = -0.08 + 0.09

Combine like terms: -0.08 + 0.09 = 0.01
0.09 + -0.6x + x2 = 0.01

Factor a perfect square on the left side:
(x + -0.3)(x + -0.3) = 0.01

Calculate the square root of the right side: 0.1

Break this problem into two subproblems by setting 
(x + -0.3) equal to 0.1 and -0.1.

Subproblem 1

x + -0.3 = 0.1 Simplifying x + -0.3 = 0.1 Reorder the terms: -0.3 + x = 0.1 Solving -0.3 + x = 0.1 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 = 0.1 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 0.1 + 0.3 x = 0.1 + 0.3 Combine like terms: 0.1 + 0.3 = 0.4 x = 0.4 Simplifying x = 0.4

Subproblem 2

x + -0.3 = -0.1 Simplifying x + -0.3 = -0.1 Reorder the terms: -0.3 + x = -0.1 Solving -0.3 + x = -0.1 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 = -0.1 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -0.1 + 0.3 x = -0.1 + 0.3 Combine like terms: -0.1 + 0.3 = 0.2 x = 0.2 Simplifying x = 0.2

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.4, 0.2}
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