X^2+1.6X-2.6=0

Solution for X^2+1.6X-2.6=0 equation:

Simplifying
X2 + 1.6X + -2.6 = 0

Reorder the terms:
-2.6 + 1.6X + X2 = 0

Solving
-2.6 + 1.6X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '2.6' to each side of the equation.
-2.6 + 1.6X + 2.6 + X2 = 0 + 2.6

Reorder the terms:
-2.6 + 2.6 + 1.6X + X2 = 0 + 2.6

Combine like terms: -2.6 + 2.6 = 0.0
0.0 + 1.6X + X2 = 0 + 2.6
1.6X + X2 = 0 + 2.6

Combine like terms: 0 + 2.6 = 2.6
1.6X + X2 = 2.6

The X term is 1.6X.  Take half its coefficient (0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
1.6X + 0.64 + X2 = 2.6 + 0.64

Reorder the terms:
0.64 + 1.6X + X2 = 2.6 + 0.64

Combine like terms: 2.6 + 0.64 = 3.24
0.64 + 1.6X + X2 = 3.24

Factor a perfect square on the left side:
(X + 0.8)(X + 0.8) = 3.24

Calculate the square root of the right side: 1.8

Break this problem into two subproblems by setting 
(X + 0.8) equal to 1.8 and -1.8.

Subproblem 1
X + 0.8 = 1.8

Simplifying
X + 0.8 = 1.8

Reorder the terms:
0.8 + X = 1.8

Solving
0.8 + X = 1.8

Solving for variable 'X'.

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

Add '-0.8' to each side of the equation.
0.8 + -0.8 + X = 1.8 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + X = 1.8 + -0.8
X = 1.8 + -0.8

Combine like terms: 1.8 + -0.8 = 1
X = 1

Simplifying
X = 1

Subproblem 2
X + 0.8 = -1.8

Simplifying
X + 0.8 = -1.8

Reorder the terms:
0.8 + X = -1.8

Solving
0.8 + X = -1.8

Solving for variable 'X'.

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

Add '-0.8' to each side of the equation.
0.8 + -0.8 + X = -1.8 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + X = -1.8 + -0.8
X = -1.8 + -0.8

Combine like terms: -1.8 + -0.8 = -2.6
X = -2.6

Simplifying
X = -2.6

Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {1, -2.6}