x-2x(x+25)=193

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Solution for x-2x(x+25)=193 equation: 


Simplifying
x + -2x(x + 25) = 193

Reorder the terms:
x + -2x(25 + x) = 193
x + (25 * -2x + x * -2x) = 193
x + (-50x + -2x2) = 193

Combine like terms: x + -50x = -49x
-49x + -2x2 = 193

Solving
-49x + -2x2 = 193

Solving for variable 'x'.

Reorder the terms:
-193 + -49x + -2x2 = 193 + -193

Combine like terms: 193 + -193 = 0
-193 + -49x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(193 + 49x + 2x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(193 + 49x + 2x2)' equal to zero and attempt to solve:

Simplifying
193 + 49x + 2x2 = 0

Solving
193 + 49x + 2x2 = 0

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

Divide each side by '2'.
96.5 + 24.5x + x2 = 0

Move the constant term to the right:

Add '-96.5' to each side of the equation.
96.5 + 24.5x + -96.5 + x2 = 0 + -96.5

Reorder the terms:
96.5 + -96.5 + 24.5x + x2 = 0 + -96.5

Combine like terms: 96.5 + -96.5 = 0.0
0.0 + 24.5x + x2 = 0 + -96.5
24.5x + x2 = 0 + -96.5

Combine like terms: 0 + -96.5 = -96.5
24.5x + x2 = -96.5

The x term is 24.5x.  Take half its coefficient (12.25).
Square it (150.0625) and add it to both sides.

Add '150.0625' to each side of the equation.
24.5x + 150.0625 + x2 = -96.5 + 150.0625

Reorder the terms:
150.0625 + 24.5x + x2 = -96.5 + 150.0625

Combine like terms: -96.5 + 150.0625 = 53.5625
150.0625 + 24.5x + x2 = 53.5625

Factor a perfect square on the left side:
(x + 12.25)(x + 12.25) = 53.5625

Calculate the square root of the right side: 7.318640584

Break this problem into two subproblems by setting 
(x + 12.25) equal to 7.318640584 and -7.318640584.


Subproblem 1
x + 12.25 = 7.318640584

Simplifying
x + 12.25 = 7.318640584

Reorder the terms:
12.25 + x = 7.318640584

Solving
12.25 + x = 7.318640584

Solving for variable 'x'.

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

Add '-12.25' to each side of the equation.
12.25 + -12.25 + x = 7.318640584 + -12.25

Combine like terms: 12.25 + -12.25 = 0.00
0.00 + x = 7.318640584 + -12.25
x = 7.318640584 + -12.25

Combine like terms: 7.318640584 + -12.25 = -4.931359416
x = -4.931359416

Simplifying
x = -4.931359416


Subproblem 2
x + 12.25 = -7.318640584

Simplifying
x + 12.25 = -7.318640584

Reorder the terms:
12.25 + x = -7.318640584

Solving
12.25 + x = -7.318640584

Solving for variable 'x'.

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

Add '-12.25' to each side of the equation.
12.25 + -12.25 + x = -7.318640584 + -12.25

Combine like terms: 12.25 + -12.25 = 0.00
0.00 + x = -7.318640584 + -12.25
x = -7.318640584 + -12.25

Combine like terms: -7.318640584 + -12.25 = -19.568640584
x = -19.568640584

Simplifying
x = -19.568640584


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-4.931359416, -19.568640584}
Solution
x = {-4.931359416, -19.568640584}

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