25x^2-104x-96=0

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Solution for 25x^2-104x-96=0 equation: 


Simplifying
25x2 + -104x + -96 = 0

Reorder the terms:
-96 + -104x + 25x2 = 0

Solving
-96 + -104x + 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'.
-3.84 + -4.16x + x2 = 0

Move the constant term to the right:

Add '3.84' to each side of the equation.
-3.84 + -4.16x + 3.84 + x2 = 0 + 3.84

Reorder the terms:
-3.84 + 3.84 + -4.16x + x2 = 0 + 3.84

Combine like terms: -3.84 + 3.84 = 0.00
0.00 + -4.16x + x2 = 0 + 3.84
-4.16x + x2 = 0 + 3.84

Combine like terms: 0 + 3.84 = 3.84
-4.16x + x2 = 3.84

The x term is -4.16x.  Take half its coefficient (-2.08).
Square it (4.3264) and add it to both sides.

Add '4.3264' to each side of the equation.
-4.16x + 4.3264 + x2 = 3.84 + 4.3264

Reorder the terms:
4.3264 + -4.16x + x2 = 3.84 + 4.3264

Combine like terms: 3.84 + 4.3264 = 8.1664
4.3264 + -4.16x + x2 = 8.1664

Factor a perfect square on the left side:
(x + -2.08)(x + -2.08) = 8.1664

Calculate the square root of the right side: 2.857691376

Break this problem into two subproblems by setting 
(x + -2.08) equal to 2.857691376 and -2.857691376.


Subproblem 1
x + -2.08 = 2.857691376

Simplifying
x + -2.08 = 2.857691376

Reorder the terms:
-2.08 + x = 2.857691376

Solving
-2.08 + x = 2.857691376

Solving for variable 'x'.

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

Add '2.08' to each side of the equation.
-2.08 + 2.08 + x = 2.857691376 + 2.08

Combine like terms: -2.08 + 2.08 = 0.00
0.00 + x = 2.857691376 + 2.08
x = 2.857691376 + 2.08

Combine like terms: 2.857691376 + 2.08 = 4.937691376
x = 4.937691376

Simplifying
x = 4.937691376


Subproblem 2
x + -2.08 = -2.857691376

Simplifying
x + -2.08 = -2.857691376

Reorder the terms:
-2.08 + x = -2.857691376

Solving
-2.08 + x = -2.857691376

Solving for variable 'x'.

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

Add '2.08' to each side of the equation.
-2.08 + 2.08 + x = -2.857691376 + 2.08

Combine like terms: -2.08 + 2.08 = 0.00
0.00 + x = -2.857691376 + 2.08
x = -2.857691376 + 2.08

Combine like terms: -2.857691376 + 2.08 = -0.777691376
x = -0.777691376

Simplifying
x = -0.777691376


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.937691376, -0.777691376}

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