6x^2+36x+10=0

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Solution for 6x^2+36x+10=0 equation: 


Simplifying
6x2 + 36x + 10 = 0

Reorder the terms:
10 + 36x + 6x2 = 0

Solving
10 + 36x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 18x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + 18x + 3x2)' equal to zero and attempt to solve:

Simplifying
5 + 18x + 3x2 = 0

Solving
5 + 18x + 3x2 = 0

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

Divide each side by '3'.
1.666666667 + 6x + x2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + 6x + -1.666666667 + x2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + 6x + x2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + 6x + x2 = 0 + -1.666666667
6x + x2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
6x + x2 = -1.666666667

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = -1.666666667 + 9

Reorder the terms:
9 + 6x + x2 = -1.666666667 + 9

Combine like terms: -1.666666667 + 9 = 7.333333333
9 + 6x + x2 = 7.333333333

Factor a perfect square on the left side:
(x + 3)(x + 3) = 7.333333333

Calculate the square root of the right side: 2.708012801

Break this problem into two subproblems by setting 
(x + 3) equal to 2.708012801 and -2.708012801.


Subproblem 1
x + 3 = 2.708012801

Simplifying
x + 3 = 2.708012801

Reorder the terms:
3 + x = 2.708012801

Solving
3 + x = 2.708012801

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 2.708012801 + -3

Combine like terms: 3 + -3 = 0
0 + x = 2.708012801 + -3
x = 2.708012801 + -3

Combine like terms: 2.708012801 + -3 = -0.291987199
x = -0.291987199

Simplifying
x = -0.291987199


Subproblem 2
x + 3 = -2.708012801

Simplifying
x + 3 = -2.708012801

Reorder the terms:
3 + x = -2.708012801

Solving
3 + x = -2.708012801

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -2.708012801 + -3

Combine like terms: 3 + -3 = 0
0 + x = -2.708012801 + -3
x = -2.708012801 + -3

Combine like terms: -2.708012801 + -3 = -5.708012801
x = -5.708012801

Simplifying
x = -5.708012801


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.291987199, -5.708012801}
Solution
x = {-0.291987199, -5.708012801}

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