0.1-0.200x=x^2

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Solution for 0.1-0.200x=x^2 equation: 


Simplifying
0.1 + -0.200x = x2

Solving
0.1 + -0.200x = x2

Solving for variable 'x'.

Combine like terms: x2 + -1x2 = 0
0.1 + -0.200x + -1x2 = 0

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

Divide each side by '-1'.
-0.1 + 0.2x + x2 = 0

Move the constant term to the right:

Add '0.1' to each side of the equation.
-0.1 + 0.2x + 0.1 + x2 = 0 + 0.1

Reorder the terms:
-0.1 + 0.1 + 0.2x + x2 = 0 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + 0.2x + x2 = 0 + 0.1
0.2x + x2 = 0 + 0.1

Combine like terms: 0 + 0.1 = 0.1
0.2x + x2 = 0.1

The x term is 0.2x.  Take half its coefficient (0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
0.2x + 0.01 + x2 = 0.1 + 0.01

Reorder the terms:
0.01 + 0.2x + x2 = 0.1 + 0.01

Combine like terms: 0.1 + 0.01 = 0.11
0.01 + 0.2x + x2 = 0.11

Factor a perfect square on the left side:
(x + 0.1)(x + 0.1) = 0.11

Calculate the square root of the right side: 0.331662479

Break this problem into two subproblems by setting 
(x + 0.1) equal to 0.331662479 and -0.331662479.


Subproblem 1
x + 0.1 = 0.331662479

Simplifying
x + 0.1 = 0.331662479

Reorder the terms:
0.1 + x = 0.331662479

Solving
0.1 + x = 0.331662479

Solving for variable 'x'.

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

Add '-0.1' to each side of the equation.
0.1 + -0.1 + x = 0.331662479 + -0.1

Combine like terms: 0.1 + -0.1 = 0.0
0.0 + x = 0.331662479 + -0.1
x = 0.331662479 + -0.1

Combine like terms: 0.331662479 + -0.1 = 0.231662479
x = 0.231662479

Simplifying
x = 0.231662479


Subproblem 2
x + 0.1 = -0.331662479

Simplifying
x + 0.1 = -0.331662479

Reorder the terms:
0.1 + x = -0.331662479

Solving
0.1 + x = -0.331662479

Solving for variable 'x'.

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

Add '-0.1' to each side of the equation.
0.1 + -0.1 + x = -0.331662479 + -0.1

Combine like terms: 0.1 + -0.1 = 0.0
0.0 + x = -0.331662479 + -0.1
x = -0.331662479 + -0.1

Combine like terms: -0.331662479 + -0.1 = -0.431662479
x = -0.431662479

Simplifying
x = -0.431662479


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.231662479, -0.431662479}

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