x^2+191x-1391.817=0

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Solution for x^2+191x-1391.817=0 equation: 


Simplifying
x2 + 191x + -1391.817 = 0

Reorder the terms:
-1391.817 + 191x + x2 = 0

Solving
-1391.817 + 191x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1391.817' to each side of the equation.
-1391.817 + 191x + 1391.817 + x2 = 0 + 1391.817

Reorder the terms:
-1391.817 + 1391.817 + 191x + x2 = 0 + 1391.817

Combine like terms: -1391.817 + 1391.817 = 0.000
0.000 + 191x + x2 = 0 + 1391.817
191x + x2 = 0 + 1391.817

Combine like terms: 0 + 1391.817 = 1391.817
191x + x2 = 1391.817

The x term is 191x.  Take half its coefficient (95.5).
Square it (9120.25) and add it to both sides.

Add '9120.25' to each side of the equation.
191x + 9120.25 + x2 = 1391.817 + 9120.25

Reorder the terms:
9120.25 + 191x + x2 = 1391.817 + 9120.25

Combine like terms: 1391.817 + 9120.25 = 10512.067
9120.25 + 191x + x2 = 10512.067

Factor a perfect square on the left side:
(x + 95.5)(x + 95.5) = 10512.067

Calculate the square root of the right side: 102.528371683

Break this problem into two subproblems by setting 
(x + 95.5) equal to 102.528371683 and -102.528371683.


Subproblem 1
x + 95.5 = 102.528371683

Simplifying
x + 95.5 = 102.528371683

Reorder the terms:
95.5 + x = 102.528371683

Solving
95.5 + x = 102.528371683

Solving for variable 'x'.

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

Add '-95.5' to each side of the equation.
95.5 + -95.5 + x = 102.528371683 + -95.5

Combine like terms: 95.5 + -95.5 = 0.0
0.0 + x = 102.528371683 + -95.5
x = 102.528371683 + -95.5

Combine like terms: 102.528371683 + -95.5 = 7.028371683
x = 7.028371683

Simplifying
x = 7.028371683


Subproblem 2
x + 95.5 = -102.528371683

Simplifying
x + 95.5 = -102.528371683

Reorder the terms:
95.5 + x = -102.528371683

Solving
95.5 + x = -102.528371683

Solving for variable 'x'.

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

Add '-95.5' to each side of the equation.
95.5 + -95.5 + x = -102.528371683 + -95.5

Combine like terms: 95.5 + -95.5 = 0.0
0.0 + x = -102.528371683 + -95.5
x = -102.528371683 + -95.5

Combine like terms: -102.528371683 + -95.5 = -198.028371683
x = -198.028371683

Simplifying
x = -198.028371683


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.028371683, -198.028371683}

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