x^2=0.12-0.12x

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Solution for x^2=0.12-0.12x equation: 


Simplifying
x2 = 0.12 + -0.12x

Solving
x2 = 0.12 + -0.12x

Solving for variable 'x'.

Reorder the terms:
-0.12 + 0.12x + x2 = 0.12 + -0.12x + -0.12 + 0.12x

Reorder the terms:
-0.12 + 0.12x + x2 = 0.12 + -0.12 + -0.12x + 0.12x

Combine like terms: 0.12 + -0.12 = 0.00
-0.12 + 0.12x + x2 = 0.00 + -0.12x + 0.12x
-0.12 + 0.12x + x2 = -0.12x + 0.12x

Combine like terms: -0.12x + 0.12x = 0.00
-0.12 + 0.12x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '0.12' to each side of the equation.
-0.12 + 0.12x + 0.12 + x2 = 0.00 + 0.12

Reorder the terms:
-0.12 + 0.12 + 0.12x + x2 = 0.00 + 0.12

Combine like terms: -0.12 + 0.12 = 0.00
0.00 + 0.12x + x2 = 0.00 + 0.12
0.12x + x2 = 0.00 + 0.12

Combine like terms: 0.00 + 0.12 = 0.12
0.12x + x2 = 0.12

The x term is 0.12x.  Take half its coefficient (0.06).
Square it (0.0036) and add it to both sides.

Add '0.0036' to each side of the equation.
0.12x + 0.0036 + x2 = 0.12 + 0.0036

Reorder the terms:
0.0036 + 0.12x + x2 = 0.12 + 0.0036

Combine like terms: 0.12 + 0.0036 = 0.1236
0.0036 + 0.12x + x2 = 0.1236

Factor a perfect square on the left side:
(x + 0.06)(x + 0.06) = 0.1236

Calculate the square root of the right side: 0.351567917

Break this problem into two subproblems by setting 
(x + 0.06) equal to 0.351567917 and -0.351567917.


Subproblem 1
x + 0.06 = 0.351567917

Simplifying
x + 0.06 = 0.351567917

Reorder the terms:
0.06 + x = 0.351567917

Solving
0.06 + x = 0.351567917

Solving for variable 'x'.

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

Add '-0.06' to each side of the equation.
0.06 + -0.06 + x = 0.351567917 + -0.06

Combine like terms: 0.06 + -0.06 = 0.00
0.00 + x = 0.351567917 + -0.06
x = 0.351567917 + -0.06

Combine like terms: 0.351567917 + -0.06 = 0.291567917
x = 0.291567917

Simplifying
x = 0.291567917


Subproblem 2
x + 0.06 = -0.351567917

Simplifying
x + 0.06 = -0.351567917

Reorder the terms:
0.06 + x = -0.351567917

Solving
0.06 + x = -0.351567917

Solving for variable 'x'.

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

Add '-0.06' to each side of the equation.
0.06 + -0.06 + x = -0.351567917 + -0.06

Combine like terms: 0.06 + -0.06 = 0.00
0.00 + x = -0.351567917 + -0.06
x = -0.351567917 + -0.06

Combine like terms: -0.351567917 + -0.06 = -0.411567917
x = -0.411567917

Simplifying
x = -0.411567917


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.291567917, -0.411567917}

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