x^2+16x+41=0

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Solution for x^2+16x+41=0 equation: 


Simplifying
x2 + 16x + 41 = 0

Reorder the terms:
41 + 16x + x2 = 0

Solving
41 + 16x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-41' to each side of the equation.
41 + 16x + -41 + x2 = 0 + -41

Reorder the terms:
41 + -41 + 16x + x2 = 0 + -41

Combine like terms: 41 + -41 = 0
0 + 16x + x2 = 0 + -41
16x + x2 = 0 + -41

Combine like terms: 0 + -41 = -41
16x + x2 = -41

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 = -41 + 64

Reorder the terms:
64 + 16x + x2 = -41 + 64

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

Factor a perfect square on the left side:
(x + 8)(x + 8) = 23

Calculate the square root of the right side: 4.795831523

Break this problem into two subproblems by setting 
(x + 8) equal to 4.795831523 and -4.795831523.


Subproblem 1
x + 8 = 4.795831523

Simplifying
x + 8 = 4.795831523

Reorder the terms:
8 + x = 4.795831523

Solving
8 + x = 4.795831523

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 = 4.795831523 + -8

Combine like terms: 8 + -8 = 0
0 + x = 4.795831523 + -8
x = 4.795831523 + -8

Combine like terms: 4.795831523 + -8 = -3.204168477
x = -3.204168477

Simplifying
x = -3.204168477


Subproblem 2
x + 8 = -4.795831523

Simplifying
x + 8 = -4.795831523

Reorder the terms:
8 + x = -4.795831523

Solving
8 + x = -4.795831523

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 = -4.795831523 + -8

Combine like terms: 8 + -8 = 0
0 + x = -4.795831523 + -8
x = -4.795831523 + -8

Combine like terms: -4.795831523 + -8 = -12.795831523
x = -12.795831523

Simplifying
x = -12.795831523


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.204168477, -12.795831523}

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