6x^2+59x-105=0

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Solution for 6x^2+59x-105=0 equation: 


Simplifying
6x2 + 59x + -105 = 0

Reorder the terms:
-105 + 59x + 6x2 = 0

Solving
-105 + 59x + 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'.
-17.5 + 9.833333333x + x2 = 0

Move the constant term to the right:

Add '17.5' to each side of the equation.
-17.5 + 9.833333333x + 17.5 + x2 = 0 + 17.5

Reorder the terms:
-17.5 + 17.5 + 9.833333333x + x2 = 0 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + 9.833333333x + x2 = 0 + 17.5
9.833333333x + x2 = 0 + 17.5

Combine like terms: 0 + 17.5 = 17.5
9.833333333x + x2 = 17.5

The x term is 9.833333333x.  Take half its coefficient (4.916666667).
Square it (24.17361111) and add it to both sides.

Add '24.17361111' to each side of the equation.
9.833333333x + 24.17361111 + x2 = 17.5 + 24.17361111

Reorder the terms:
24.17361111 + 9.833333333x + x2 = 17.5 + 24.17361111

Combine like terms: 17.5 + 24.17361111 = 41.67361111
24.17361111 + 9.833333333x + x2 = 41.67361111

Factor a perfect square on the left side:
(x + 4.916666667)(x + 4.916666667) = 41.67361111

Calculate the square root of the right side: 6.455510136

Break this problem into two subproblems by setting 
(x + 4.916666667) equal to 6.455510136 and -6.455510136.


Subproblem 1
x + 4.916666667 = 6.455510136

Simplifying
x + 4.916666667 = 6.455510136

Reorder the terms:
4.916666667 + x = 6.455510136

Solving
4.916666667 + x = 6.455510136

Solving for variable 'x'.

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

Add '-4.916666667' to each side of the equation.
4.916666667 + -4.916666667 + x = 6.455510136 + -4.916666667

Combine like terms: 4.916666667 + -4.916666667 = 0.000000000
0.000000000 + x = 6.455510136 + -4.916666667
x = 6.455510136 + -4.916666667

Combine like terms: 6.455510136 + -4.916666667 = 1.538843469
x = 1.538843469

Simplifying
x = 1.538843469


Subproblem 2
x + 4.916666667 = -6.455510136

Simplifying
x + 4.916666667 = -6.455510136

Reorder the terms:
4.916666667 + x = -6.455510136

Solving
4.916666667 + x = -6.455510136

Solving for variable 'x'.

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

Add '-4.916666667' to each side of the equation.
4.916666667 + -4.916666667 + x = -6.455510136 + -4.916666667

Combine like terms: 4.916666667 + -4.916666667 = 0.000000000
0.000000000 + x = -6.455510136 + -4.916666667
x = -6.455510136 + -4.916666667

Combine like terms: -6.455510136 + -4.916666667 = -11.372176803
x = -11.372176803

Simplifying
x = -11.372176803


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.538843469, -11.372176803}

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