x^2+0.6x-0.16=0

Solution for x^2+0.6x-0.16=0 equation:

Simplifying
x2 + 0.6x + -0.16 = 0

Reorder the terms:
-0.16 + 0.6x + x2 = 0

Solving
-0.16 + 0.6x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.16' to each side of the equation.
-0.16 + 0.6x + 0.16 + x2 = 0 + 0.16

Reorder the terms:
-0.16 + 0.16 + 0.6x + x2 = 0 + 0.16

Combine like terms: -0.16 + 0.16 = 0.00
0.00 + 0.6x + x2 = 0 + 0.16
0.6x + x2 = 0 + 0.16

Combine like terms: 0 + 0.16 = 0.16
0.6x + x2 = 0.16

The x term is 0.6x.  Take half its coefficient (0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
0.6x + 0.09 + x2 = 0.16 + 0.09

Reorder the terms:
0.09 + 0.6x + x2 = 0.16 + 0.09

Combine like terms: 0.16 + 0.09 = 0.25
0.09 + 0.6x + x2 = 0.25

Factor a perfect square on the left side:
(x + 0.3)(x + 0.3) = 0.25

Calculate the square root of the right side: 0.5

Break this problem into two subproblems by setting 
(x + 0.3) equal to 0.5 and -0.5.

Subproblem 1
x + 0.3 = 0.5

Simplifying
x + 0.3 = 0.5

Reorder the terms:
0.3 + x = 0.5

Solving
0.3 + x = 0.5

Solving for variable 'x'.

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

Add '-0.3' to each side of the equation.
0.3 + -0.3 + x = 0.5 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + x = 0.5 + -0.3
x = 0.5 + -0.3

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

Simplifying
x = 0.2

Subproblem 2
x + 0.3 = -0.5

Simplifying
x + 0.3 = -0.5

Reorder the terms:
0.3 + x = -0.5

Solving
0.3 + x = -0.5

Solving for variable 'x'.

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

Add '-0.3' to each side of the equation.
0.3 + -0.3 + x = -0.5 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + x = -0.5 + -0.3
x = -0.5 + -0.3

Combine like terms: -0.5 + -0.3 = -0.8
x = -0.8

Simplifying
x = -0.8

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.2, -0.8}