25X^2-40X-19=0

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Solution for 25X^2-40X-19=0 equation: 


Simplifying
25X2 + -40X + -19 = 0

Reorder the terms:
-19 + -40X + 25X2 = 0

Solving
-19 + -40X + 25X2 = 0

Solving for variable 'X'.

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

Divide each side by '25'.
-0.76 + -1.6X + X2 = 0

Move the constant term to the right:

Add '0.76' to each side of the equation.
-0.76 + -1.6X + 0.76 + X2 = 0 + 0.76

Reorder the terms:
-0.76 + 0.76 + -1.6X + X2 = 0 + 0.76

Combine like terms: -0.76 + 0.76 = 0.00
0.00 + -1.6X + X2 = 0 + 0.76
-1.6X + X2 = 0 + 0.76

Combine like terms: 0 + 0.76 = 0.76
-1.6X + X2 = 0.76

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 = 0.76 + 0.64

Reorder the terms:
0.64 + -1.6X + X2 = 0.76 + 0.64

Combine like terms: 0.76 + 0.64 = 1.4
0.64 + -1.6X + X2 = 1.4

Factor a perfect square on the left side:
(X + -0.8)(X + -0.8) = 1.4

Calculate the square root of the right side: 1.183215957

Break this problem into two subproblems by setting 
(X + -0.8) equal to 1.183215957 and -1.183215957.


Subproblem 1
X + -0.8 = 1.183215957

Simplifying
X + -0.8 = 1.183215957

Reorder the terms:
-0.8 + X = 1.183215957

Solving
-0.8 + X = 1.183215957

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 = 1.183215957 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + X = 1.183215957 + 0.8
X = 1.183215957 + 0.8

Combine like terms: 1.183215957 + 0.8 = 1.983215957
X = 1.983215957

Simplifying
X = 1.983215957


Subproblem 2
X + -0.8 = -1.183215957

Simplifying
X + -0.8 = -1.183215957

Reorder the terms:
-0.8 + X = -1.183215957

Solving
-0.8 + X = -1.183215957

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 = -1.183215957 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + X = -1.183215957 + 0.8
X = -1.183215957 + 0.8

Combine like terms: -1.183215957 + 0.8 = -0.383215957
X = -0.383215957

Simplifying
X = -0.383215957


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {1.983215957, -0.383215957}

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