x^2+0.4x-0.21=0

Solution for x^2+0.4x-0.21=0 equation:

Simplifying
x2 + 0.4x + -0.21 = 0

Reorder the terms:
-0.21 + 0.4x + x2 = 0

Solving
-0.21 + 0.4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.21' to each side of the equation.
-0.21 + 0.4x + 0.21 + x2 = 0 + 0.21

Reorder the terms:
-0.21 + 0.21 + 0.4x + x2 = 0 + 0.21

Combine like terms: -0.21 + 0.21 = 0.00
0.00 + 0.4x + x2 = 0 + 0.21
0.4x + x2 = 0 + 0.21

Combine like terms: 0 + 0.21 = 0.21
0.4x + x2 = 0.21

The x term is 0.4x.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4x + 0.04 + x2 = 0.21 + 0.04

Reorder the terms:
0.04 + 0.4x + x2 = 0.21 + 0.04

Combine like terms: 0.21 + 0.04 = 0.25
0.04 + 0.4x + x2 = 0.25

Factor a perfect square on the left side:
(x + 0.2)(x + 0.2) = 0.25

Calculate the square root of the right side: 0.5

Break this problem into two subproblems by setting 
(x + 0.2) equal to 0.5 and -0.5.

Subproblem 1
x + 0.2 = 0.5

Simplifying
x + 0.2 = 0.5

Reorder the terms:
0.2 + x = 0.5

Solving
0.2 + x = 0.5

Solving for variable 'x'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + x = 0.5 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + x = 0.5 + -0.2
x = 0.5 + -0.2

Combine like terms: 0.5 + -0.2 = 0.3
x = 0.3

Simplifying
x = 0.3

Subproblem 2
x + 0.2 = -0.5

Simplifying
x + 0.2 = -0.5

Reorder the terms:
0.2 + x = -0.5

Solving
0.2 + x = -0.5

Solving for variable 'x'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + x = -0.5 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + x = -0.5 + -0.2
x = -0.5 + -0.2

Combine like terms: -0.5 + -0.2 = -0.7
x = -0.7

Simplifying
x = -0.7

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.3, -0.7}