x^2-0.6x-2.8=0

Solution for x^2-0.6x-2.8=0 equation:

Simplifying
x2 + -0.6x + -2.8 = 0

Reorder the terms:
-2.8 + -0.6x + x2 = 0

Solving
-2.8 + -0.6x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '2.8' to each side of the equation.
-2.8 + -0.6x + 2.8 + x2 = 0 + 2.8

Reorder the terms:
-2.8 + 2.8 + -0.6x + x2 = 0 + 2.8

Combine like terms: -2.8 + 2.8 = 0.0
0.0 + -0.6x + x2 = 0 + 2.8
-0.6x + x2 = 0 + 2.8

Combine like terms: 0 + 2.8 = 2.8
-0.6x + x2 = 2.8

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 = 2.8 + 0.09

Reorder the terms:
0.09 + -0.6x + x2 = 2.8 + 0.09

Combine like terms: 2.8 + 0.09 = 2.89
0.09 + -0.6x + x2 = 2.89

Factor a perfect square on the left side:
(x + -0.3)(x + -0.3) = 2.89

Calculate the square root of the right side: 1.7

Break this problem into two subproblems by setting 
(x + -0.3) equal to 1.7 and -1.7.

Subproblem 1
x + -0.3 = 1.7

Simplifying
x + -0.3 = 1.7

Reorder the terms:
-0.3 + x = 1.7

Solving
-0.3 + x = 1.7

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 = 1.7 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + x = 1.7 + 0.3
x = 1.7 + 0.3

Combine like terms: 1.7 + 0.3 = 2
x = 2

Simplifying
x = 2

Subproblem 2
x + -0.3 = -1.7

Simplifying
x + -0.3 = -1.7

Reorder the terms:
-0.3 + x = -1.7

Solving
-0.3 + x = -1.7

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 = -1.7 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + x = -1.7 + 0.3
x = -1.7 + 0.3

Combine like terms: -1.7 + 0.3 = -1.4
x = -1.4

Simplifying
x = -1.4

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2, -1.4}