x^2+18x+40=0

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Solution for x^2+18x+40=0 equation: 


Simplifying
x2 + 18x + 40 = 0

Reorder the terms:
40 + 18x + x2 = 0

Solving
40 + 18x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-40' to each side of the equation.
40 + 18x + -40 + x2 = 0 + -40

Reorder the terms:
40 + -40 + 18x + x2 = 0 + -40

Combine like terms: 40 + -40 = 0
0 + 18x + x2 = 0 + -40
18x + x2 = 0 + -40

Combine like terms: 0 + -40 = -40
18x + x2 = -40

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 = -40 + 81

Reorder the terms:
81 + 18x + x2 = -40 + 81

Combine like terms: -40 + 81 = 41
81 + 18x + x2 = 41

Factor a perfect square on the left side:
(x + 9)(x + 9) = 41

Calculate the square root of the right side: 6.403124237

Break this problem into two subproblems by setting 
(x + 9) equal to 6.403124237 and -6.403124237.


Subproblem 1
x + 9 = 6.403124237

Simplifying
x + 9 = 6.403124237

Reorder the terms:
9 + x = 6.403124237

Solving
9 + x = 6.403124237

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 = 6.403124237 + -9

Combine like terms: 9 + -9 = 0
0 + x = 6.403124237 + -9
x = 6.403124237 + -9

Combine like terms: 6.403124237 + -9 = -2.596875763
x = -2.596875763

Simplifying
x = -2.596875763


Subproblem 2
x + 9 = -6.403124237

Simplifying
x + 9 = -6.403124237

Reorder the terms:
9 + x = -6.403124237

Solving
9 + x = -6.403124237

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 = -6.403124237 + -9

Combine like terms: 9 + -9 = 0
0 + x = -6.403124237 + -9
x = -6.403124237 + -9

Combine like terms: -6.403124237 + -9 = -15.403124237
x = -15.403124237

Simplifying
x = -15.403124237


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.596875763, -15.403124237}

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