x^2-0.2=-0.06x

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Solution for x^2-0.2=-0.06x equation: 


Simplifying
x2 + -0.2 = -0.06x

Reorder the terms:
-0.2 + x2 = -0.06x

Solving
-0.2 + x2 = -0.06x

Solving for variable 'x'.

Reorder the terms:
-0.2 + 0.06x + x2 = -0.06x + 0.06x

Combine like terms: -0.06x + 0.06x = 0.00
-0.2 + 0.06x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + 0.06x + 0.2 + x2 = 0.00 + 0.2

Reorder the terms:
-0.2 + 0.2 + 0.06x + x2 = 0.00 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + 0.06x + x2 = 0.00 + 0.2
0.06x + x2 = 0.00 + 0.2

Combine like terms: 0.00 + 0.2 = 0.2
0.06x + x2 = 0.2

The x term is 0.06x.  Take half its coefficient (0.03).
Square it (0.0009) and add it to both sides.

Add '0.0009' to each side of the equation.
0.06x + 0.0009 + x2 = 0.2 + 0.0009

Reorder the terms:
0.0009 + 0.06x + x2 = 0.2 + 0.0009

Combine like terms: 0.2 + 0.0009 = 0.2009
0.0009 + 0.06x + x2 = 0.2009

Factor a perfect square on the left side:
(x + 0.03)(x + 0.03) = 0.2009

Calculate the square root of the right side: 0.448218697

Break this problem into two subproblems by setting 
(x + 0.03) equal to 0.448218697 and -0.448218697.


Subproblem 1
x + 0.03 = 0.448218697

Simplifying
x + 0.03 = 0.448218697

Reorder the terms:
0.03 + x = 0.448218697

Solving
0.03 + x = 0.448218697

Solving for variable 'x'.

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

Add '-0.03' to each side of the equation.
0.03 + -0.03 + x = 0.448218697 + -0.03

Combine like terms: 0.03 + -0.03 = 0.00
0.00 + x = 0.448218697 + -0.03
x = 0.448218697 + -0.03

Combine like terms: 0.448218697 + -0.03 = 0.418218697
x = 0.418218697

Simplifying
x = 0.418218697


Subproblem 2
x + 0.03 = -0.448218697

Simplifying
x + 0.03 = -0.448218697

Reorder the terms:
0.03 + x = -0.448218697

Solving
0.03 + x = -0.448218697

Solving for variable 'x'.

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

Add '-0.03' to each side of the equation.
0.03 + -0.03 + x = -0.448218697 + -0.03

Combine like terms: 0.03 + -0.03 = 0.00
0.00 + x = -0.448218697 + -0.03
x = -0.448218697 + -0.03

Combine like terms: -0.448218697 + -0.03 = -0.478218697
x = -0.478218697

Simplifying
x = -0.478218697


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.418218697, -0.478218697}

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