6x^2+65x-74=0

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Solution for 6x^2+65x-74=0 equation: 


Simplifying
6x2 + 65x + -74 = 0

Reorder the terms:
-74 + 65x + 6x2 = 0

Solving
-74 + 65x + 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'.
-12.33333333 + 10.83333333x + x2 = 0

Move the constant term to the right:

Add '12.33333333' to each side of the equation.
-12.33333333 + 10.83333333x + 12.33333333 + x2 = 0 + 12.33333333

Reorder the terms:
-12.33333333 + 12.33333333 + 10.83333333x + x2 = 0 + 12.33333333

Combine like terms: -12.33333333 + 12.33333333 = 0.00000000
0.00000000 + 10.83333333x + x2 = 0 + 12.33333333
10.83333333x + x2 = 0 + 12.33333333

Combine like terms: 0 + 12.33333333 = 12.33333333
10.83333333x + x2 = 12.33333333

The x term is 10.83333333x.  Take half its coefficient (5.416666665).
Square it (29.34027776) and add it to both sides.

Add '29.34027776' to each side of the equation.
10.83333333x + 29.34027776 + x2 = 12.33333333 + 29.34027776

Reorder the terms:
29.34027776 + 10.83333333x + x2 = 12.33333333 + 29.34027776

Combine like terms: 12.33333333 + 29.34027776 = 41.67361109
29.34027776 + 10.83333333x + x2 = 41.67361109

Factor a perfect square on the left side:
(x + 5.416666665)(x + 5.416666665) = 41.67361109

Calculate the square root of the right side: 6.455510134

Break this problem into two subproblems by setting 
(x + 5.416666665) equal to 6.455510134 and -6.455510134.


Subproblem 1
x + 5.416666665 = 6.455510134

Simplifying
x + 5.416666665 = 6.455510134

Reorder the terms:
5.416666665 + x = 6.455510134

Solving
5.416666665 + x = 6.455510134

Solving for variable 'x'.

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

Add '-5.416666665' to each side of the equation.
5.416666665 + -5.416666665 + x = 6.455510134 + -5.416666665

Combine like terms: 5.416666665 + -5.416666665 = 0.000000000
0.000000000 + x = 6.455510134 + -5.416666665
x = 6.455510134 + -5.416666665

Combine like terms: 6.455510134 + -5.416666665 = 1.038843469
x = 1.038843469

Simplifying
x = 1.038843469


Subproblem 2
x + 5.416666665 = -6.455510134

Simplifying
x + 5.416666665 = -6.455510134

Reorder the terms:
5.416666665 + x = -6.455510134

Solving
5.416666665 + x = -6.455510134

Solving for variable 'x'.

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

Add '-5.416666665' to each side of the equation.
5.416666665 + -5.416666665 + x = -6.455510134 + -5.416666665

Combine like terms: 5.416666665 + -5.416666665 = 0.000000000
0.000000000 + x = -6.455510134 + -5.416666665
x = -6.455510134 + -5.416666665

Combine like terms: -6.455510134 + -5.416666665 = -11.872176799
x = -11.872176799

Simplifying
x = -11.872176799


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.038843469, -11.872176799}

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