6x^2-73x-130=0

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Solution for 6x^2-73x-130=0 equation: 


Simplifying
6x2 + -73x + -130 = 0

Reorder the terms:
-130 + -73x + 6x2 = 0

Solving
-130 + -73x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
-21.66666667 + -12.16666667x + x2 = 0

Move the constant term to the right:

Add '21.66666667' to each side of the equation.
-21.66666667 + -12.16666667x + 21.66666667 + x2 = 0 + 21.66666667

Reorder the terms:
-21.66666667 + 21.66666667 + -12.16666667x + x2 = 0 + 21.66666667

Combine like terms: -21.66666667 + 21.66666667 = 0.00000000
0.00000000 + -12.16666667x + x2 = 0 + 21.66666667
-12.16666667x + x2 = 0 + 21.66666667

Combine like terms: 0 + 21.66666667 = 21.66666667
-12.16666667x + x2 = 21.66666667

The x term is -12.16666667x.  Take half its coefficient (-6.083333335).
Square it (37.00694446) and add it to both sides.

Add '37.00694446' to each side of the equation.
-12.16666667x + 37.00694446 + x2 = 21.66666667 + 37.00694446

Reorder the terms:
37.00694446 + -12.16666667x + x2 = 21.66666667 + 37.00694446

Combine like terms: 21.66666667 + 37.00694446 = 58.67361113
37.00694446 + -12.16666667x + x2 = 58.67361113

Factor a perfect square on the left side:
(x + -6.083333335)(x + -6.083333335) = 58.67361113

Calculate the square root of the right side: 7.659870177

Break this problem into two subproblems by setting 
(x + -6.083333335) equal to 7.659870177 and -7.659870177.


Subproblem 1
x + -6.083333335 = 7.659870177

Simplifying
x + -6.083333335 = 7.659870177

Reorder the terms:
-6.083333335 + x = 7.659870177

Solving
-6.083333335 + x = 7.659870177

Solving for variable 'x'.

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

Add '6.083333335' to each side of the equation.
-6.083333335 + 6.083333335 + x = 7.659870177 + 6.083333335

Combine like terms: -6.083333335 + 6.083333335 = 0.000000000
0.000000000 + x = 7.659870177 + 6.083333335
x = 7.659870177 + 6.083333335

Combine like terms: 7.659870177 + 6.083333335 = 13.743203512
x = 13.743203512

Simplifying
x = 13.743203512


Subproblem 2
x + -6.083333335 = -7.659870177

Simplifying
x + -6.083333335 = -7.659870177

Reorder the terms:
-6.083333335 + x = -7.659870177

Solving
-6.083333335 + x = -7.659870177

Solving for variable 'x'.

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

Add '6.083333335' to each side of the equation.
-6.083333335 + 6.083333335 + x = -7.659870177 + 6.083333335

Combine like terms: -6.083333335 + 6.083333335 = 0.000000000
0.000000000 + x = -7.659870177 + 6.083333335
x = -7.659870177 + 6.083333335

Combine like terms: -7.659870177 + 6.083333335 = -1.576536842
x = -1.576536842

Simplifying
x = -1.576536842


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.743203512, -1.576536842}

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