x^2+23x+14=0

Solution for x^2+23x+14=0 equation:

Simplifying
x2 + 23x + 14 = 0

Reorder the terms:
14 + 23x + x2 = 0

Solving
14 + 23x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-14' to each side of the equation.
14 + 23x + -14 + x2 = 0 + -14

Reorder the terms:
14 + -14 + 23x + x2 = 0 + -14

Combine like terms: 14 + -14 = 0
0 + 23x + x2 = 0 + -14
23x + x2 = 0 + -14

Combine like terms: 0 + -14 = -14
23x + x2 = -14

The x term is 23x.  Take half its coefficient (11.5).
Square it (132.25) and add it to both sides.

Add '132.25' to each side of the equation.
23x + 132.25 + x2 = -14 + 132.25

Reorder the terms:
132.25 + 23x + x2 = -14 + 132.25

Combine like terms: -14 + 132.25 = 118.25
132.25 + 23x + x2 = 118.25

Factor a perfect square on the left side:
(x + 11.5)(x + 11.5) = 118.25

Calculate the square root of the right side: 10.874281585

Break this problem into two subproblems by setting 
(x + 11.5) equal to 10.874281585 and -10.874281585.

Subproblem 1
x + 11.5 = 10.874281585

Simplifying
x + 11.5 = 10.874281585

Reorder the terms:
11.5 + x = 10.874281585

Solving
11.5 + x = 10.874281585

Solving for variable 'x'.

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

Add '-11.5' to each side of the equation.
11.5 + -11.5 + x = 10.874281585 + -11.5

Combine like terms: 11.5 + -11.5 = 0.0
0.0 + x = 10.874281585 + -11.5
x = 10.874281585 + -11.5

Combine like terms: 10.874281585 + -11.5 = -0.625718415
x = -0.625718415

Simplifying
x = -0.625718415

Subproblem 2
x + 11.5 = -10.874281585

Simplifying
x + 11.5 = -10.874281585

Reorder the terms:
11.5 + x = -10.874281585

Solving
11.5 + x = -10.874281585

Solving for variable 'x'.

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

Add '-11.5' to each side of the equation.
11.5 + -11.5 + x = -10.874281585 + -11.5

Combine like terms: 11.5 + -11.5 = 0.0
0.0 + x = -10.874281585 + -11.5
x = -10.874281585 + -11.5

Combine like terms: -10.874281585 + -11.5 = -22.374281585
x = -22.374281585

Simplifying
x = -22.374281585

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.625718415, -22.374281585}