x^2+0.6x-0.72=0

Solution for x^2+0.6x-0.72=0 equation:

Simplifying
x2 + 0.6x + -0.72 = 0

Reorder the terms:
-0.72 + 0.6x + x2 = 0

Solving
-0.72 + 0.6x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.72' to each side of the equation.
-0.72 + 0.6x + 0.72 + x2 = 0 + 0.72

Reorder the terms:
-0.72 + 0.72 + 0.6x + x2 = 0 + 0.72

Combine like terms: -0.72 + 0.72 = 0.00
0.00 + 0.6x + x2 = 0 + 0.72
0.6x + x2 = 0 + 0.72

Combine like terms: 0 + 0.72 = 0.72
0.6x + x2 = 0.72

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 = 0.72 + 0.09

Reorder the terms:
0.09 + 0.6x + x2 = 0.72 + 0.09

Combine like terms: 0.72 + 0.09 = 0.81
0.09 + 0.6x + x2 = 0.81

Factor a perfect square on the left side:
(x + 0.3)(x + 0.3) = 0.81

Calculate the square root of the right side: 0.9

Break this problem into two subproblems by setting 
(x + 0.3) equal to 0.9 and -0.9.

Subproblem 1
x + 0.3 = 0.9

Simplifying
x + 0.3 = 0.9

Reorder the terms:
0.3 + x = 0.9

Solving
0.3 + x = 0.9

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 = 0.9 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + x = 0.9 + -0.3
x = 0.9 + -0.3

Combine like terms: 0.9 + -0.3 = 0.6
x = 0.6

Simplifying
x = 0.6

Subproblem 2
x + 0.3 = -0.9

Simplifying
x + 0.3 = -0.9

Reorder the terms:
0.3 + x = -0.9

Solving
0.3 + x = -0.9

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 = -0.9 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + x = -0.9 + -0.3
x = -0.9 + -0.3

Combine like terms: -0.9 + -0.3 = -1.2
x = -1.2

Simplifying
x = -1.2

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.6, -1.2}