x^2+0.6x-1.35=0

Solution for x^2+0.6x-1.35=0 equation:

Simplifying
x2 + 0.6x + -1.35 = 0

Reorder the terms:
-1.35 + 0.6x + x2 = 0

Solving
-1.35 + 0.6x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1.35' to each side of the equation.
-1.35 + 0.6x + 1.35 + x2 = 0 + 1.35

Reorder the terms:
-1.35 + 1.35 + 0.6x + x2 = 0 + 1.35

Combine like terms: -1.35 + 1.35 = 0.00
0.00 + 0.6x + x2 = 0 + 1.35
0.6x + x2 = 0 + 1.35

Combine like terms: 0 + 1.35 = 1.35
0.6x + x2 = 1.35

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 = 1.35 + 0.09

Reorder the terms:
0.09 + 0.6x + x2 = 1.35 + 0.09

Combine like terms: 1.35 + 0.09 = 1.44
0.09 + 0.6x + x2 = 1.44

Factor a perfect square on the left side:
(x + 0.3)(x + 0.3) = 1.44

Calculate the square root of the right side: 1.2

Break this problem into two subproblems by setting 
(x + 0.3) equal to 1.2 and -1.2.

Subproblem 1
x + 0.3 = 1.2

Simplifying
x + 0.3 = 1.2

Reorder the terms:
0.3 + x = 1.2

Solving
0.3 + x = 1.2

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 = 1.2 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + x = 1.2 + -0.3
x = 1.2 + -0.3

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

Simplifying
x = 0.9

Subproblem 2
x + 0.3 = -1.2

Simplifying
x + 0.3 = -1.2

Reorder the terms:
0.3 + x = -1.2

Solving
0.3 + x = -1.2

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 = -1.2 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + x = -1.2 + -0.3
x = -1.2 + -0.3

Combine like terms: -1.2 + -0.3 = -1.5
x = -1.5

Simplifying
x = -1.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.9, -1.5}