x^2+0.2x-0.36=0

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Solution for x^2+0.2x-0.36=0 equation: 


Simplifying
x2 + 0.2x + -0.36 = 0

Reorder the terms:
-0.36 + 0.2x + x2 = 0

Solving
-0.36 + 0.2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.36' to each side of the equation.
-0.36 + 0.2x + 0.36 + x2 = 0 + 0.36

Reorder the terms:
-0.36 + 0.36 + 0.2x + x2 = 0 + 0.36

Combine like terms: -0.36 + 0.36 = 0.00
0.00 + 0.2x + x2 = 0 + 0.36
0.2x + x2 = 0 + 0.36

Combine like terms: 0 + 0.36 = 0.36
0.2x + x2 = 0.36

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 = 0.36 + 0.01

Reorder the terms:
0.01 + 0.2x + x2 = 0.36 + 0.01

Combine like terms: 0.36 + 0.01 = 0.37
0.01 + 0.2x + x2 = 0.37

Factor a perfect square on the left side:
(x + 0.1)(x + 0.1) = 0.37

Calculate the square root of the right side: 0.608276253

Break this problem into two subproblems by setting 
(x + 0.1) equal to 0.608276253 and -0.608276253.


Subproblem 1
x + 0.1 = 0.608276253

Simplifying
x + 0.1 = 0.608276253

Reorder the terms:
0.1 + x = 0.608276253

Solving
0.1 + x = 0.608276253

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 = 0.608276253 + -0.1

Combine like terms: 0.1 + -0.1 = 0.0
0.0 + x = 0.608276253 + -0.1
x = 0.608276253 + -0.1

Combine like terms: 0.608276253 + -0.1 = 0.508276253
x = 0.508276253

Simplifying
x = 0.508276253


Subproblem 2
x + 0.1 = -0.608276253

Simplifying
x + 0.1 = -0.608276253

Reorder the terms:
0.1 + x = -0.608276253

Solving
0.1 + x = -0.608276253

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 = -0.608276253 + -0.1

Combine like terms: 0.1 + -0.1 = 0.0
0.0 + x = -0.608276253 + -0.1
x = -0.608276253 + -0.1

Combine like terms: -0.608276253 + -0.1 = -0.708276253
x = -0.708276253

Simplifying
x = -0.708276253


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.508276253, -0.708276253}

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