x^2-0.6x-0.27=0

Solution for x^2-0.6x-0.27=0 equation:

Simplifying
x2 + -0.6x + -0.27 = 0

Reorder the terms:
-0.27 + -0.6x + x2 = 0

Solving
-0.27 + -0.6x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.27' to each side of the equation.
-0.27 + -0.6x + 0.27 + x2 = 0 + 0.27

Reorder the terms:
-0.27 + 0.27 + -0.6x + x2 = 0 + 0.27

Combine like terms: -0.27 + 0.27 = 0.00
0.00 + -0.6x + x2 = 0 + 0.27
-0.6x + x2 = 0 + 0.27

Combine like terms: 0 + 0.27 = 0.27
-0.6x + x2 = 0.27

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 = 0.27 + 0.09

Reorder the terms:
0.09 + -0.6x + x2 = 0.27 + 0.09

Combine like terms: 0.27 + 0.09 = 0.36
0.09 + -0.6x + x2 = 0.36

Factor a perfect square on the left side:
(x + -0.3)(x + -0.3) = 0.36

Calculate the square root of the right side: 0.6

Break this problem into two subproblems by setting 
(x + -0.3) equal to 0.6 and -0.6.

Subproblem 1
x + -0.3 = 0.6

Simplifying
x + -0.3 = 0.6

Reorder the terms:
-0.3 + x = 0.6

Solving
-0.3 + x = 0.6

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 = 0.6 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + x = 0.6 + 0.3
x = 0.6 + 0.3

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

Simplifying
x = 0.9

Subproblem 2
x + -0.3 = -0.6

Simplifying
x + -0.3 = -0.6

Reorder the terms:
-0.3 + x = -0.6

Solving
-0.3 + x = -0.6

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 = -0.6 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + x = -0.6 + 0.3
x = -0.6 + 0.3

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

Simplifying
x = -0.3

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.9, -0.3}