2x^2+36x+72=0

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Solution for 2x^2+36x+72=0 equation: 


Simplifying
2x2 + 36x + 72 = 0

Reorder the terms:
72 + 36x + 2x2 = 0

Solving
72 + 36x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(36 + 18x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(36 + 18x + x2)' equal to zero and attempt to solve:

Simplifying
36 + 18x + x2 = 0

Solving
36 + 18x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-36' to each side of the equation.
36 + 18x + -36 + x2 = 0 + -36

Reorder the terms:
36 + -36 + 18x + x2 = 0 + -36

Combine like terms: 36 + -36 = 0
0 + 18x + x2 = 0 + -36
18x + x2 = 0 + -36

Combine like terms: 0 + -36 = -36
18x + x2 = -36

The x term is 18x.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18x + 81 + x2 = -36 + 81

Reorder the terms:
81 + 18x + x2 = -36 + 81

Combine like terms: -36 + 81 = 45
81 + 18x + x2 = 45

Factor a perfect square on the left side:
(x + 9)(x + 9) = 45

Calculate the square root of the right side: 6.708203933

Break this problem into two subproblems by setting 
(x + 9) equal to 6.708203933 and -6.708203933.


Subproblem 1
x + 9 = 6.708203933

Simplifying
x + 9 = 6.708203933

Reorder the terms:
9 + x = 6.708203933

Solving
9 + x = 6.708203933

Solving for variable 'x'.

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

Add '-9' to each side of the equation.
9 + -9 + x = 6.708203933 + -9

Combine like terms: 9 + -9 = 0
0 + x = 6.708203933 + -9
x = 6.708203933 + -9

Combine like terms: 6.708203933 + -9 = -2.291796067
x = -2.291796067

Simplifying
x = -2.291796067


Subproblem 2
x + 9 = -6.708203933

Simplifying
x + 9 = -6.708203933

Reorder the terms:
9 + x = -6.708203933

Solving
9 + x = -6.708203933

Solving for variable 'x'.

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

Add '-9' to each side of the equation.
9 + -9 + x = -6.708203933 + -9

Combine like terms: 9 + -9 = 0
0 + x = -6.708203933 + -9
x = -6.708203933 + -9

Combine like terms: -6.708203933 + -9 = -15.708203933
x = -15.708203933

Simplifying
x = -15.708203933


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.291796067, -15.708203933}
Solution
x = {-2.291796067, -15.708203933}

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