6x^2+5x+7+36x=

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Solution for 6x^2+5x+7+36x= equation: 


Simplifying
6x2 + 5x + 7 + 36x = 0

Reorder the terms:
7 + 5x + 36x + 6x2 = 0

Combine like terms: 5x + 36x = 41x
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 = -0.175224944
x = -0.175224944

Simplifying
x = -0.175224944


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 = -6.65810839
x = -6.65810839

Simplifying
x = -6.65810839


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

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