x^2+77.20715x-5578.344647062639=0

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Solution for x^2+77.20715x-5578.344647062639=0 equation: 


Simplifying
x2 + 77.20715x + -5578.344647062639 = 0

Reorder the terms:
-5578.344647062639 + 77.20715x + x2 = 0

Solving
-5578.344647062639 + 77.20715x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '5578.344647062639' to each side of the equation.
-5578.344647062639 + 77.20715x + 5578.344647062639 + x2 = 0 + 5578.344647062639

Reorder the terms:
-5578.344647062639 + 5578.344647062639 + 77.20715x + x2 = 0 + 5578.344647062639

Combine like terms: -5578.344647062639 + 5578.344647062639 = 0.000000000000
0.000000000000 + 77.20715x + x2 = 0 + 5578.344647062639
77.20715x + x2 = 0 + 5578.344647062639

Combine like terms: 0 + 5578.344647062639 = 5578.344647062639
77.20715x + x2 = 5578.344647062639

The x term is 77.20715x.  Take half its coefficient (38.603575).
Square it (1490.236003) and add it to both sides.

Add '1490.236003' to each side of the equation.
77.20715x + 1490.236003 + x2 = 5578.344647062639 + 1490.236003

Reorder the terms:
1490.236003 + 77.20715x + x2 = 5578.344647062639 + 1490.236003

Combine like terms: 5578.344647062639 + 1490.236003 = 7068.580650062639
1490.236003 + 77.20715x + x2 = 7068.580650062639

Factor a perfect square on the left side:
(x + 38.603575)(x + 38.603575) = 7068.580650062639

Calculate the square root of the right side: 84.074851472

Break this problem into two subproblems by setting 
(x + 38.603575) equal to 84.074851472 and -84.074851472.


Subproblem 1
x + 38.603575 = 84.074851472

Simplifying
x + 38.603575 = 84.074851472

Reorder the terms:
38.603575 + x = 84.074851472

Solving
38.603575 + x = 84.074851472

Solving for variable 'x'.

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

Add '-38.603575' to each side of the equation.
38.603575 + -38.603575 + x = 84.074851472 + -38.603575

Combine like terms: 38.603575 + -38.603575 = 0.000000
0.000000 + x = 84.074851472 + -38.603575
x = 84.074851472 + -38.603575

Combine like terms: 84.074851472 + -38.603575 = 45.471276472
x = 45.471276472

Simplifying
x = 45.471276472


Subproblem 2
x + 38.603575 = -84.074851472

Simplifying
x + 38.603575 = -84.074851472

Reorder the terms:
38.603575 + x = -84.074851472

Solving
38.603575 + x = -84.074851472

Solving for variable 'x'.

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

Add '-38.603575' to each side of the equation.
38.603575 + -38.603575 + x = -84.074851472 + -38.603575

Combine like terms: 38.603575 + -38.603575 = 0.000000
0.000000 + x = -84.074851472 + -38.603575
x = -84.074851472 + -38.603575

Combine like terms: -84.074851472 + -38.603575 = -122.678426472
x = -122.678426472

Simplifying
x = -122.678426472


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {45.471276472, -122.678426472}

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