.25X^2+2.6X-116.4=0

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Solution for .25X^2+2.6X-116.4=0 equation: 


Simplifying
0.25X2 + 2.6X + -116.4 = 0

Reorder the terms:
-116.4 + 2.6X + 0.25X2 = 0

Solving
-116.4 + 2.6X + 0.25X2 = 0

Solving for variable 'X'.

Begin completing the square.  Divide all terms by
0.25 the coefficient of the squared term: 

Divide each side by '0.25'.
-465.6 + 10.4X + X2 = 0

Move the constant term to the right:

Add '465.6' to each side of the equation.
-465.6 + 10.4X + 465.6 + X2 = 0 + 465.6

Reorder the terms:
-465.6 + 465.6 + 10.4X + X2 = 0 + 465.6

Combine like terms: -465.6 + 465.6 = 0.0
0.0 + 10.4X + X2 = 0 + 465.6
10.4X + X2 = 0 + 465.6

Combine like terms: 0 + 465.6 = 465.6
10.4X + X2 = 465.6

The X term is 10.4X.  Take half its coefficient (5.2).
Square it (27.04) and add it to both sides.

Add '27.04' to each side of the equation.
10.4X + 27.04 + X2 = 465.6 + 27.04

Reorder the terms:
27.04 + 10.4X + X2 = 465.6 + 27.04

Combine like terms: 465.6 + 27.04 = 492.64
27.04 + 10.4X + X2 = 492.64

Factor a perfect square on the left side:
(X + 5.2)(X + 5.2) = 492.64

Calculate the square root of the right side: 22.195495038

Break this problem into two subproblems by setting 
(X + 5.2) equal to 22.195495038 and -22.195495038.


Subproblem 1
X + 5.2 = 22.195495038

Simplifying
X + 5.2 = 22.195495038

Reorder the terms:
5.2 + X = 22.195495038

Solving
5.2 + X = 22.195495038

Solving for variable 'X'.

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

Add '-5.2' to each side of the equation.
5.2 + -5.2 + X = 22.195495038 + -5.2

Combine like terms: 5.2 + -5.2 = 0.0
0.0 + X = 22.195495038 + -5.2
X = 22.195495038 + -5.2

Combine like terms: 22.195495038 + -5.2 = 16.995495038
X = 16.995495038

Simplifying
X = 16.995495038


Subproblem 2
X + 5.2 = -22.195495038

Simplifying
X + 5.2 = -22.195495038

Reorder the terms:
5.2 + X = -22.195495038

Solving
5.2 + X = -22.195495038

Solving for variable 'X'.

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

Add '-5.2' to each side of the equation.
5.2 + -5.2 + X = -22.195495038 + -5.2

Combine like terms: 5.2 + -5.2 = 0.0
0.0 + X = -22.195495038 + -5.2
X = -22.195495038 + -5.2

Combine like terms: -22.195495038 + -5.2 = -27.395495038
X = -27.395495038

Simplifying
X = -27.395495038


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {16.995495038, -27.395495038}

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