2x^2+36x+100=0

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Solution for 2x^2+36x+100=0 equation: 


Simplifying
2x2 + 36x + 100 = 0

Reorder the terms:
100 + 36x + 2x2 = 0

Solving
100 + 36x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(50 + 18x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(50 + 18x + x2)' equal to zero and attempt to solve:

Simplifying
50 + 18x + x2 = 0

Solving
50 + 18x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-50' to each side of the equation.
50 + 18x + -50 + x2 = 0 + -50

Reorder the terms:
50 + -50 + 18x + x2 = 0 + -50

Combine like terms: 50 + -50 = 0
0 + 18x + x2 = 0 + -50
18x + x2 = 0 + -50

Combine like terms: 0 + -50 = -50
18x + x2 = -50

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 = -50 + 81

Reorder the terms:
81 + 18x + x2 = -50 + 81

Combine like terms: -50 + 81 = 31
81 + 18x + x2 = 31

Factor a perfect square on the left side:
(x + 9)(x + 9) = 31

Calculate the square root of the right side: 5.567764363

Break this problem into two subproblems by setting 
(x + 9) equal to 5.567764363 and -5.567764363.


Subproblem 1
x + 9 = 5.567764363

Simplifying
x + 9 = 5.567764363

Reorder the terms:
9 + x = 5.567764363

Solving
9 + x = 5.567764363

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 = 5.567764363 + -9

Combine like terms: 9 + -9 = 0
0 + x = 5.567764363 + -9
x = 5.567764363 + -9

Combine like terms: 5.567764363 + -9 = -3.432235637
x = -3.432235637

Simplifying
x = -3.432235637


Subproblem 2
x + 9 = -5.567764363

Simplifying
x + 9 = -5.567764363

Reorder the terms:
9 + x = -5.567764363

Solving
9 + x = -5.567764363

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 = -5.567764363 + -9

Combine like terms: 9 + -9 = 0
0 + x = -5.567764363 + -9
x = -5.567764363 + -9

Combine like terms: -5.567764363 + -9 = -14.567764363
x = -14.567764363

Simplifying
x = -14.567764363


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.432235637, -14.567764363}
Solution
x = {-3.432235637, -14.567764363}

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