0.02=(x+0.2)*x

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Solution for 0.02=(x+0.2)*x equation: 


Simplifying
0.02 = (x + 0.2) * x

Reorder the terms:
0.02 = (0.2 + x) * x

Reorder the terms for easier multiplication:
0.02 = x(0.2 + x)
0.02 = (0.2 * x + x * x)
0.02 = (0.2x + x2)

Solving
0.02 = 0.2x + x2

Solving for variable 'x'.

Reorder the terms:
0.02 + -0.2x + -1x2 = 0.2x + -0.2x + x2 + -1x2

Combine like terms: 0.2x + -0.2x = 0.0
0.02 + -0.2x + -1x2 = 0.0 + x2 + -1x2
0.02 + -0.2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
0.02 + -0.2x + -1x2 = 0

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

Divide each side by '-1'.
-0.02 + 0.2x + x2 = 0

Move the constant term to the right:

Add '0.02' to each side of the equation.
-0.02 + 0.2x + 0.02 + x2 = 0 + 0.02

Reorder the terms:
-0.02 + 0.02 + 0.2x + x2 = 0 + 0.02

Combine like terms: -0.02 + 0.02 = 0.00
0.00 + 0.2x + x2 = 0 + 0.02
0.2x + x2 = 0 + 0.02

Combine like terms: 0 + 0.02 = 0.02
0.2x + x2 = 0.02

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 = 0.02 + 0.01

Reorder the terms:
0.01 + 0.2x + x2 = 0.02 + 0.01

Combine like terms: 0.02 + 0.01 = 0.03
0.01 + 0.2x + x2 = 0.03

Factor a perfect square on the left side:
(x + 0.1)(x + 0.1) = 0.03

Calculate the square root of the right side: 0.173205081

Break this problem into two subproblems by setting 
(x + 0.1) equal to 0.173205081 and -0.173205081.


Subproblem 1
x + 0.1 = 0.173205081

Simplifying
x + 0.1 = 0.173205081

Reorder the terms:
0.1 + x = 0.173205081

Solving
0.1 + x = 0.173205081

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 = 0.173205081 + -0.1

Combine like terms: 0.1 + -0.1 = 0.0
0.0 + x = 0.173205081 + -0.1
x = 0.173205081 + -0.1

Combine like terms: 0.173205081 + -0.1 = 0.073205081
x = 0.073205081

Simplifying
x = 0.073205081


Subproblem 2
x + 0.1 = -0.173205081

Simplifying
x + 0.1 = -0.173205081

Reorder the terms:
0.1 + x = -0.173205081

Solving
0.1 + x = -0.173205081

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 = -0.173205081 + -0.1

Combine like terms: 0.1 + -0.1 = 0.0
0.0 + x = -0.173205081 + -0.1
x = -0.173205081 + -0.1

Combine like terms: -0.173205081 + -0.1 = -0.273205081
x = -0.273205081

Simplifying
x = -0.273205081


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.073205081, -0.273205081}

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