2x^2+36x+16=0

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Solution for 2x^2+36x+16=0 equation: 


Simplifying
2x2 + 36x + 16 = 0

Reorder the terms:
16 + 36x + 2x2 = 0

Solving
16 + 36x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + 18x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(8 + 18x + x2)' equal to zero and attempt to solve:

Simplifying
8 + 18x + x2 = 0

Solving
8 + 18x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + 18x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + 18x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 18x + x2 = 0 + -8
18x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
18x + x2 = -8

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 = -8 + 81

Reorder the terms:
81 + 18x + x2 = -8 + 81

Combine like terms: -8 + 81 = 73
81 + 18x + x2 = 73

Factor a perfect square on the left side:
(x + 9)(x + 9) = 73

Calculate the square root of the right side: 8.544003745

Break this problem into two subproblems by setting 
(x + 9) equal to 8.544003745 and -8.544003745.


Subproblem 1
x + 9 = 8.544003745

Simplifying
x + 9 = 8.544003745

Reorder the terms:
9 + x = 8.544003745

Solving
9 + x = 8.544003745

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 = 8.544003745 + -9

Combine like terms: 9 + -9 = 0
0 + x = 8.544003745 + -9
x = 8.544003745 + -9

Combine like terms: 8.544003745 + -9 = -0.455996255
x = -0.455996255

Simplifying
x = -0.455996255


Subproblem 2
x + 9 = -8.544003745

Simplifying
x + 9 = -8.544003745

Reorder the terms:
9 + x = -8.544003745

Solving
9 + x = -8.544003745

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 = -8.544003745 + -9

Combine like terms: 9 + -9 = 0
0 + x = -8.544003745 + -9
x = -8.544003745 + -9

Combine like terms: -8.544003745 + -9 = -17.544003745
x = -17.544003745

Simplifying
x = -17.544003745


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.455996255, -17.544003745}
Solution
x = {-0.455996255, -17.544003745}

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