x^2-0.2x-0.03=0

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Solution for x^2-0.2x-0.03=0 equation: 


Simplifying
x2 + -0.2x + -0.03 = 0

Reorder the terms:
-0.03 + -0.2x + x2 = 0

Solving
-0.03 + -0.2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.03' to each side of the equation.
-0.03 + -0.2x + 0.03 + x2 = 0 + 0.03

Reorder the terms:
-0.03 + 0.03 + -0.2x + x2 = 0 + 0.03

Combine like terms: -0.03 + 0.03 = 0.00
0.00 + -0.2x + x2 = 0 + 0.03
-0.2x + x2 = 0 + 0.03

Combine like terms: 0 + 0.03 = 0.03
-0.2x + x2 = 0.03

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 = 0.03 + 0.01

Reorder the terms:
0.01 + -0.2x + x2 = 0.03 + 0.01

Combine like terms: 0.03 + 0.01 = 0.04
0.01 + -0.2x + x2 = 0.04

Factor a perfect square on the left side:
(x + -0.1)(x + -0.1) = 0.04

Calculate the square root of the right side: 0.2

Break this problem into two subproblems by setting 
(x + -0.1) equal to 0.2 and -0.2.


Subproblem 1
x + -0.1 = 0.2

Simplifying
x + -0.1 = 0.2

Reorder the terms:
-0.1 + x = 0.2

Solving
-0.1 + x = 0.2

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 = 0.2 + 0.1

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

Combine like terms: 0.2 + 0.1 = 0.3
x = 0.3

Simplifying
x = 0.3


Subproblem 2
x + -0.1 = -0.2

Simplifying
x + -0.1 = -0.2

Reorder the terms:
-0.1 + x = -0.2

Solving
-0.1 + x = -0.2

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 = -0.2 + 0.1

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

Combine like terms: -0.2 + 0.1 = -0.1
x = -0.1

Simplifying
x = -0.1


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.3, -0.1}

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