2x^2+23x+36=0

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Solution for 2x^2+23x+36=0 equation: 


Simplifying
2x2 + 23x + 36 = 0

Reorder the terms:
36 + 23x + 2x2 = 0

Solving
36 + 23x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
18 + 11.5x + x2 = 0

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + 11.5x + -18 + x2 = 0 + -18

Reorder the terms:
18 + -18 + 11.5x + x2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + 11.5x + x2 = 0 + -18
11.5x + x2 = 0 + -18

Combine like terms: 0 + -18 = -18
11.5x + x2 = -18

The x term is 11.5x.  Take half its coefficient (5.75).
Square it (33.0625) and add it to both sides.

Add '33.0625' to each side of the equation.
11.5x + 33.0625 + x2 = -18 + 33.0625

Reorder the terms:
33.0625 + 11.5x + x2 = -18 + 33.0625

Combine like terms: -18 + 33.0625 = 15.0625
33.0625 + 11.5x + x2 = 15.0625

Factor a perfect square on the left side:
(x + 5.75)(x + 5.75) = 15.0625

Calculate the square root of the right side: 3.881043674

Break this problem into two subproblems by setting 
(x + 5.75) equal to 3.881043674 and -3.881043674.


Subproblem 1
x + 5.75 = 3.881043674

Simplifying
x + 5.75 = 3.881043674

Reorder the terms:
5.75 + x = 3.881043674

Solving
5.75 + x = 3.881043674

Solving for variable 'x'.

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

Add '-5.75' to each side of the equation.
5.75 + -5.75 + x = 3.881043674 + -5.75

Combine like terms: 5.75 + -5.75 = 0.00
0.00 + x = 3.881043674 + -5.75
x = 3.881043674 + -5.75

Combine like terms: 3.881043674 + -5.75 = -1.868956326
x = -1.868956326

Simplifying
x = -1.868956326


Subproblem 2
x + 5.75 = -3.881043674

Simplifying
x + 5.75 = -3.881043674

Reorder the terms:
5.75 + x = -3.881043674

Solving
5.75 + x = -3.881043674

Solving for variable 'x'.

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

Add '-5.75' to each side of the equation.
5.75 + -5.75 + x = -3.881043674 + -5.75

Combine like terms: 5.75 + -5.75 = 0.00
0.00 + x = -3.881043674 + -5.75
x = -3.881043674 + -5.75

Combine like terms: -3.881043674 + -5.75 = -9.631043674
x = -9.631043674

Simplifying
x = -9.631043674


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.868956326, -9.631043674}

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