-6x^2+41x-7=0

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Solution for -6x^2+41x-7=0 equation: 


Simplifying
-6x2 + 41x + -7 = 0

Reorder the terms:
-7 + 41x + -6x2 = 0

Solving
-7 + 41x + -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'.
1.166666667 + -6.833333333x + x2 = 0

Move the constant term to the right:

Add '-1.166666667' to each side of the equation.
1.166666667 + -6.833333333x + -1.166666667 + x2 = 0 + -1.166666667

Reorder the terms:
1.166666667 + -1.166666667 + -6.833333333x + x2 = 0 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + -6.833333333x + x2 = 0 + -1.166666667
-6.833333333x + x2 = 0 + -1.166666667

Combine like terms: 0 + -1.166666667 = -1.166666667
-6.833333333x + x2 = -1.166666667

The x term is -6.833333333x.  Take half its coefficient (-3.416666667).
Square it (11.67361111) and add it to both sides.

Add '11.67361111' to each side of the equation.
-6.833333333x + 11.67361111 + x2 = -1.166666667 + 11.67361111

Reorder the terms:
11.67361111 + -6.833333333x + x2 = -1.166666667 + 11.67361111

Combine like terms: -1.166666667 + 11.67361111 = 10.506944443
11.67361111 + -6.833333333x + x2 = 10.506944443

Factor a perfect square on the left side:
(x + -3.416666667)(x + -3.416666667) = 10.506944443

Calculate the square root of the right side: 3.241441723

Break this problem into two subproblems by setting 
(x + -3.416666667) equal to 3.241441723 and -3.241441723.


Subproblem 1
x + -3.416666667 = 3.241441723

Simplifying
x + -3.416666667 = 3.241441723

Reorder the terms:
-3.416666667 + x = 3.241441723

Solving
-3.416666667 + x = 3.241441723

Solving for variable 'x'.

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

Add '3.416666667' to each side of the equation.
-3.416666667 + 3.416666667 + x = 3.241441723 + 3.416666667

Combine like terms: -3.416666667 + 3.416666667 = 0.000000000
0.000000000 + x = 3.241441723 + 3.416666667
x = 3.241441723 + 3.416666667

Combine like terms: 3.241441723 + 3.416666667 = 6.65810839
x = 6.65810839

Simplifying
x = 6.65810839


Subproblem 2
x + -3.416666667 = -3.241441723

Simplifying
x + -3.416666667 = -3.241441723

Reorder the terms:
-3.416666667 + x = -3.241441723

Solving
-3.416666667 + x = -3.241441723

Solving for variable 'x'.

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

Add '3.416666667' to each side of the equation.
-3.416666667 + 3.416666667 + x = -3.241441723 + 3.416666667

Combine like terms: -3.416666667 + 3.416666667 = 0.000000000
0.000000000 + x = -3.241441723 + 3.416666667
x = -3.241441723 + 3.416666667

Combine like terms: -3.241441723 + 3.416666667 = 0.175224944
x = 0.175224944

Simplifying
x = 0.175224944


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.65810839, 0.175224944}

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