x^2+16x+23=0

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Solution for x^2+16x+23=0 equation: 


Simplifying
x2 + 16x + 23 = 0

Reorder the terms:
23 + 16x + x2 = 0

Solving
23 + 16x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-23' to each side of the equation.
23 + 16x + -23 + x2 = 0 + -23

Reorder the terms:
23 + -23 + 16x + x2 = 0 + -23

Combine like terms: 23 + -23 = 0
0 + 16x + x2 = 0 + -23
16x + x2 = 0 + -23

Combine like terms: 0 + -23 = -23
16x + x2 = -23

The x term is 16x.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16x + 64 + x2 = -23 + 64

Reorder the terms:
64 + 16x + x2 = -23 + 64

Combine like terms: -23 + 64 = 41
64 + 16x + x2 = 41

Factor a perfect square on the left side:
(x + 8)(x + 8) = 41

Calculate the square root of the right side: 6.403124237

Break this problem into two subproblems by setting 
(x + 8) equal to 6.403124237 and -6.403124237.


Subproblem 1
x + 8 = 6.403124237

Simplifying
x + 8 = 6.403124237

Reorder the terms:
8 + x = 6.403124237

Solving
8 + x = 6.403124237

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = 6.403124237 + -8

Combine like terms: 8 + -8 = 0
0 + x = 6.403124237 + -8
x = 6.403124237 + -8

Combine like terms: 6.403124237 + -8 = -1.596875763
x = -1.596875763

Simplifying
x = -1.596875763


Subproblem 2
x + 8 = -6.403124237

Simplifying
x + 8 = -6.403124237

Reorder the terms:
8 + x = -6.403124237

Solving
8 + x = -6.403124237

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = -6.403124237 + -8

Combine like terms: 8 + -8 = 0
0 + x = -6.403124237 + -8
x = -6.403124237 + -8

Combine like terms: -6.403124237 + -8 = -14.403124237
x = -14.403124237

Simplifying
x = -14.403124237


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.596875763, -14.403124237}

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