2x^2-25x-5=0

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Solution for 2x^2-25x-5=0 equation: 


Simplifying
2x2 + -25x + -5 = 0

Reorder the terms:
-5 + -25x + 2x2 = 0

Solving
-5 + -25x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-2.5 + -12.5x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + -12.5x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + -12.5x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + -12.5x + x2 = 0 + 2.5
-12.5x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
-12.5x + x2 = 2.5

The x term is -12.5x.  Take half its coefficient (-6.25).
Square it (39.0625) and add it to both sides.

Add '39.0625' to each side of the equation.
-12.5x + 39.0625 + x2 = 2.5 + 39.0625

Reorder the terms:
39.0625 + -12.5x + x2 = 2.5 + 39.0625

Combine like terms: 2.5 + 39.0625 = 41.5625
39.0625 + -12.5x + x2 = 41.5625

Factor a perfect square on the left side:
(x + -6.25)(x + -6.25) = 41.5625

Calculate the square root of the right side: 6.446898479

Break this problem into two subproblems by setting 
(x + -6.25) equal to 6.446898479 and -6.446898479.


Subproblem 1
x + -6.25 = 6.446898479

Simplifying
x + -6.25 = 6.446898479

Reorder the terms:
-6.25 + x = 6.446898479

Solving
-6.25 + x = 6.446898479

Solving for variable 'x'.

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

Add '6.25' to each side of the equation.
-6.25 + 6.25 + x = 6.446898479 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + x = 6.446898479 + 6.25
x = 6.446898479 + 6.25

Combine like terms: 6.446898479 + 6.25 = 12.696898479
x = 12.696898479

Simplifying
x = 12.696898479


Subproblem 2
x + -6.25 = -6.446898479

Simplifying
x + -6.25 = -6.446898479

Reorder the terms:
-6.25 + x = -6.446898479

Solving
-6.25 + x = -6.446898479

Solving for variable 'x'.

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

Add '6.25' to each side of the equation.
-6.25 + 6.25 + x = -6.446898479 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + x = -6.446898479 + 6.25
x = -6.446898479 + 6.25

Combine like terms: -6.446898479 + 6.25 = -0.196898479
x = -0.196898479

Simplifying
x = -0.196898479


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.696898479, -0.196898479}

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