x^2+31x+18=0

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Solution for x^2+31x+18=0 equation: 


Simplifying
x2 + 31x + 18 = 0

Reorder the terms:
18 + 31x + x2 = 0

Solving
18 + 31x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + 31x + -18 + x2 = 0 + -18

Reorder the terms:
18 + -18 + 31x + x2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + 31x + x2 = 0 + -18
31x + x2 = 0 + -18

Combine like terms: 0 + -18 = -18
31x + x2 = -18

The x term is 31x.  Take half its coefficient (15.5).
Square it (240.25) and add it to both sides.

Add '240.25' to each side of the equation.
31x + 240.25 + x2 = -18 + 240.25

Reorder the terms:
240.25 + 31x + x2 = -18 + 240.25

Combine like terms: -18 + 240.25 = 222.25
240.25 + 31x + x2 = 222.25

Factor a perfect square on the left side:
(x + 15.5)(x + 15.5) = 222.25

Calculate the square root of the right side: 14.908051516

Break this problem into two subproblems by setting 
(x + 15.5) equal to 14.908051516 and -14.908051516.


Subproblem 1
x + 15.5 = 14.908051516

Simplifying
x + 15.5 = 14.908051516

Reorder the terms:
15.5 + x = 14.908051516

Solving
15.5 + x = 14.908051516

Solving for variable 'x'.

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

Add '-15.5' to each side of the equation.
15.5 + -15.5 + x = 14.908051516 + -15.5

Combine like terms: 15.5 + -15.5 = 0.0
0.0 + x = 14.908051516 + -15.5
x = 14.908051516 + -15.5

Combine like terms: 14.908051516 + -15.5 = -0.591948484
x = -0.591948484

Simplifying
x = -0.591948484


Subproblem 2
x + 15.5 = -14.908051516

Simplifying
x + 15.5 = -14.908051516

Reorder the terms:
15.5 + x = -14.908051516

Solving
15.5 + x = -14.908051516

Solving for variable 'x'.

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

Add '-15.5' to each side of the equation.
15.5 + -15.5 + x = -14.908051516 + -15.5

Combine like terms: 15.5 + -15.5 = 0.0
0.0 + x = -14.908051516 + -15.5
x = -14.908051516 + -15.5

Combine like terms: -14.908051516 + -15.5 = -30.408051516
x = -30.408051516

Simplifying
x = -30.408051516


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.591948484, -30.408051516}

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