x^2+16x+29=0

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Solution for x^2+16x+29=0 equation: 


Simplifying
x2 + 16x + 29 = 0

Reorder the terms:
29 + 16x + x2 = 0

Solving
29 + 16x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-29' to each side of the equation.
29 + 16x + -29 + x2 = 0 + -29

Reorder the terms:
29 + -29 + 16x + x2 = 0 + -29

Combine like terms: 29 + -29 = 0
0 + 16x + x2 = 0 + -29
16x + x2 = 0 + -29

Combine like terms: 0 + -29 = -29
16x + x2 = -29

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 = -29 + 64

Reorder the terms:
64 + 16x + x2 = -29 + 64

Combine like terms: -29 + 64 = 35
64 + 16x + x2 = 35

Factor a perfect square on the left side:
(x + 8)(x + 8) = 35

Calculate the square root of the right side: 5.916079783

Break this problem into two subproblems by setting 
(x + 8) equal to 5.916079783 and -5.916079783.


Subproblem 1
x + 8 = 5.916079783

Simplifying
x + 8 = 5.916079783

Reorder the terms:
8 + x = 5.916079783

Solving
8 + x = 5.916079783

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 = 5.916079783 + -8

Combine like terms: 8 + -8 = 0
0 + x = 5.916079783 + -8
x = 5.916079783 + -8

Combine like terms: 5.916079783 + -8 = -2.083920217
x = -2.083920217

Simplifying
x = -2.083920217


Subproblem 2
x + 8 = -5.916079783

Simplifying
x + 8 = -5.916079783

Reorder the terms:
8 + x = -5.916079783

Solving
8 + x = -5.916079783

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 = -5.916079783 + -8

Combine like terms: 8 + -8 = 0
0 + x = -5.916079783 + -8
x = -5.916079783 + -8

Combine like terms: -5.916079783 + -8 = -13.916079783
x = -13.916079783

Simplifying
x = -13.916079783


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.083920217, -13.916079783}

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