X^2+1.3X-2.6=0

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Solution for X^2+1.3X-2.6=0 equation: 


Simplifying
X2 + 1.3X + -2.6 = 0

Reorder the terms:
-2.6 + 1.3X + X2 = 0

Solving
-2.6 + 1.3X + 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 + 1.3X + 2.6 + X2 = 0 + 2.6

Reorder the terms:
-2.6 + 2.6 + 1.3X + X2 = 0 + 2.6

Combine like terms: -2.6 + 2.6 = 0.0
0.0 + 1.3X + X2 = 0 + 2.6
1.3X + X2 = 0 + 2.6

Combine like terms: 0 + 2.6 = 2.6
1.3X + X2 = 2.6

The X term is 1.3X.  Take half its coefficient (0.65).
Square it (0.4225) and add it to both sides.

Add '0.4225' to each side of the equation.
1.3X + 0.4225 + X2 = 2.6 + 0.4225

Reorder the terms:
0.4225 + 1.3X + X2 = 2.6 + 0.4225

Combine like terms: 2.6 + 0.4225 = 3.0225
0.4225 + 1.3X + X2 = 3.0225

Factor a perfect square on the left side:
(X + 0.65)(X + 0.65) = 3.0225

Calculate the square root of the right side: 1.738533865

Break this problem into two subproblems by setting 
(X + 0.65) equal to 1.738533865 and -1.738533865.


Subproblem 1
X + 0.65 = 1.738533865

Simplifying
X + 0.65 = 1.738533865

Reorder the terms:
0.65 + X = 1.738533865

Solving
0.65 + X = 1.738533865

Solving for variable 'X'.

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

Add '-0.65' to each side of the equation.
0.65 + -0.65 + X = 1.738533865 + -0.65

Combine like terms: 0.65 + -0.65 = 0.00
0.00 + X = 1.738533865 + -0.65
X = 1.738533865 + -0.65

Combine like terms: 1.738533865 + -0.65 = 1.088533865
X = 1.088533865

Simplifying
X = 1.088533865


Subproblem 2
X + 0.65 = -1.738533865

Simplifying
X + 0.65 = -1.738533865

Reorder the terms:
0.65 + X = -1.738533865

Solving
0.65 + X = -1.738533865

Solving for variable 'X'.

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

Add '-0.65' to each side of the equation.
0.65 + -0.65 + X = -1.738533865 + -0.65

Combine like terms: 0.65 + -0.65 = 0.00
0.00 + X = -1.738533865 + -0.65
X = -1.738533865 + -0.65

Combine like terms: -1.738533865 + -0.65 = -2.388533865
X = -2.388533865

Simplifying
X = -2.388533865


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {1.088533865, -2.388533865}

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