4x^2-20x-25-169=0

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Solution for 4x^2-20x-25-169=0 equation: 


Simplifying
4x2 + -20x + -25 + -169 = 0

Reorder the terms:
-25 + -169 + -20x + 4x2 = 0

Combine like terms: -25 + -169 = -194
-194 + -20x + 4x2 = 0

Solving
-194 + -20x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-97 + -10x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-97 + -10x + 2x2)' equal to zero and attempt to solve:

Simplifying
-97 + -10x + 2x2 = 0

Solving
-97 + -10x + 2x2 = 0

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

Divide each side by '2'.
-48.5 + -5x + x2 = 0

Move the constant term to the right:

Add '48.5' to each side of the equation.
-48.5 + -5x + 48.5 + x2 = 0 + 48.5

Reorder the terms:
-48.5 + 48.5 + -5x + x2 = 0 + 48.5

Combine like terms: -48.5 + 48.5 = 0.0
0.0 + -5x + x2 = 0 + 48.5
-5x + x2 = 0 + 48.5

Combine like terms: 0 + 48.5 = 48.5
-5x + x2 = 48.5

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 48.5 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 48.5 + 6.25

Combine like terms: 48.5 + 6.25 = 54.75
6.25 + -5x + x2 = 54.75

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 54.75

Calculate the square root of the right side: 7.399324293

Break this problem into two subproblems by setting 
(x + -2.5) equal to 7.399324293 and -7.399324293.


Subproblem 1
x + -2.5 = 7.399324293

Simplifying
x + -2.5 = 7.399324293

Reorder the terms:
-2.5 + x = 7.399324293

Solving
-2.5 + x = 7.399324293

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 7.399324293 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 7.399324293 + 2.5
x = 7.399324293 + 2.5

Combine like terms: 7.399324293 + 2.5 = 9.899324293
x = 9.899324293

Simplifying
x = 9.899324293


Subproblem 2
x + -2.5 = -7.399324293

Simplifying
x + -2.5 = -7.399324293

Reorder the terms:
-2.5 + x = -7.399324293

Solving
-2.5 + x = -7.399324293

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -7.399324293 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -7.399324293 + 2.5
x = -7.399324293 + 2.5

Combine like terms: -7.399324293 + 2.5 = -4.899324293
x = -4.899324293

Simplifying
x = -4.899324293


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.899324293, -4.899324293}
Solution
x = {9.899324293, -4.899324293}

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