x^2+191x-32470=0

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Solution for x^2+191x-32470=0 equation: 


Simplifying
x2 + 191x + -32470 = 0

Reorder the terms:
-32470 + 191x + x2 = 0

Solving
-32470 + 191x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '32470' to each side of the equation.
-32470 + 191x + 32470 + x2 = 0 + 32470

Reorder the terms:
-32470 + 32470 + 191x + x2 = 0 + 32470

Combine like terms: -32470 + 32470 = 0
0 + 191x + x2 = 0 + 32470
191x + x2 = 0 + 32470

Combine like terms: 0 + 32470 = 32470
191x + x2 = 32470

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 = 32470 + 9120.25

Reorder the terms:
9120.25 + 191x + x2 = 32470 + 9120.25

Combine like terms: 32470 + 9120.25 = 41590.25
9120.25 + 191x + x2 = 41590.25

Factor a perfect square on the left side:
(x + 95.5)(x + 95.5) = 41590.25

Calculate the square root of the right side: 203.936877489

Break this problem into two subproblems by setting 
(x + 95.5) equal to 203.936877489 and -203.936877489.


Subproblem 1
x + 95.5 = 203.936877489

Simplifying
x + 95.5 = 203.936877489

Reorder the terms:
95.5 + x = 203.936877489

Solving
95.5 + x = 203.936877489

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 = 203.936877489 + -95.5

Combine like terms: 95.5 + -95.5 = 0.0
0.0 + x = 203.936877489 + -95.5
x = 203.936877489 + -95.5

Combine like terms: 203.936877489 + -95.5 = 108.436877489
x = 108.436877489

Simplifying
x = 108.436877489


Subproblem 2
x + 95.5 = -203.936877489

Simplifying
x + 95.5 = -203.936877489

Reorder the terms:
95.5 + x = -203.936877489

Solving
95.5 + x = -203.936877489

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 = -203.936877489 + -95.5

Combine like terms: 95.5 + -95.5 = 0.0
0.0 + x = -203.936877489 + -95.5
x = -203.936877489 + -95.5

Combine like terms: -203.936877489 + -95.5 = -299.436877489
x = -299.436877489

Simplifying
x = -299.436877489


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {108.436877489, -299.436877489}

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