x^2+73x-39338=0

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Solution for x^2+73x-39338=0 equation:


Simplifying
x2 + 73x + -39338 = 0

Reorder the terms:
-39338 + 73x + x2 = 0

Solving
-39338 + 73x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '39338' to each side of the equation.
-39338 + 73x + 39338 + x2 = 0 + 39338

Reorder the terms:
-39338 + 39338 + 73x + x2 = 0 + 39338

Combine like terms: -39338 + 39338 = 0
0 + 73x + x2 = 0 + 39338
73x + x2 = 0 + 39338

Combine like terms: 0 + 39338 = 39338
73x + x2 = 39338

The x term is 73x.  Take half its coefficient (36.5).
Square it (1332.25) and add it to both sides.

Add '1332.25' to each side of the equation.
73x + 1332.25 + x2 = 39338 + 1332.25

Reorder the terms:
1332.25 + 73x + x2 = 39338 + 1332.25

Combine like terms: 39338 + 1332.25 = 40670.25
1332.25 + 73x + x2 = 40670.25

Factor a perfect square on the left side:
(x + 36.5)(x + 36.5) = 40670.25

Calculate the square root of the right side: 201.668663902

Break this problem into two subproblems by setting 
(x + 36.5) equal to 201.668663902 and -201.668663902.


Subproblem 1
x + 36.5 = 201.668663902

Simplifying
x + 36.5 = 201.668663902

Reorder the terms:
36.5 + x = 201.668663902

Solving
36.5 + x = 201.668663902

Solving for variable 'x'.

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

Add '-36.5' to each side of the equation.
36.5 + -36.5 + x = 201.668663902 + -36.5

Combine like terms: 36.5 + -36.5 = 0.0
0.0 + x = 201.668663902 + -36.5
x = 201.668663902 + -36.5

Combine like terms: 201.668663902 + -36.5 = 165.168663902
x = 165.168663902

Simplifying
x = 165.168663902


Subproblem 2
x + 36.5 = -201.668663902

Simplifying
x + 36.5 = -201.668663902

Reorder the terms:
36.5 + x = -201.668663902

Solving
36.5 + x = -201.668663902

Solving for variable 'x'.

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

Add '-36.5' to each side of the equation.
36.5 + -36.5 + x = -201.668663902 + -36.5

Combine like terms: 36.5 + -36.5 = 0.0
0.0 + x = -201.668663902 + -36.5
x = -201.668663902 + -36.5

Combine like terms: -201.668663902 + -36.5 = -238.168663902
x = -238.168663902

Simplifying
x = -238.168663902


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {165.168663902, -238.168663902}

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