x^2+20x+29=0

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Solution for x^2+20x+29=0 equation: 


Simplifying
x2 + 20x + 29 = 0

Reorder the terms:
29 + 20x + x2 = 0

Solving
29 + 20x + 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 + 20x + -29 + x2 = 0 + -29

Reorder the terms:
29 + -29 + 20x + x2 = 0 + -29

Combine like terms: 29 + -29 = 0
0 + 20x + x2 = 0 + -29
20x + x2 = 0 + -29

Combine like terms: 0 + -29 = -29
20x + x2 = -29

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = -29 + 100

Reorder the terms:
100 + 20x + x2 = -29 + 100

Combine like terms: -29 + 100 = 71
100 + 20x + x2 = 71

Factor a perfect square on the left side:
(x + 10)(x + 10) = 71

Calculate the square root of the right side: 8.426149773

Break this problem into two subproblems by setting 
(x + 10) equal to 8.426149773 and -8.426149773.


Subproblem 1
x + 10 = 8.426149773

Simplifying
x + 10 = 8.426149773

Reorder the terms:
10 + x = 8.426149773

Solving
10 + x = 8.426149773

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = 8.426149773 + -10

Combine like terms: 10 + -10 = 0
0 + x = 8.426149773 + -10
x = 8.426149773 + -10

Combine like terms: 8.426149773 + -10 = -1.573850227
x = -1.573850227

Simplifying
x = -1.573850227


Subproblem 2
x + 10 = -8.426149773

Simplifying
x + 10 = -8.426149773

Reorder the terms:
10 + x = -8.426149773

Solving
10 + x = -8.426149773

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = -8.426149773 + -10

Combine like terms: 10 + -10 = 0
0 + x = -8.426149773 + -10
x = -8.426149773 + -10

Combine like terms: -8.426149773 + -10 = -18.426149773
x = -18.426149773

Simplifying
x = -18.426149773


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.573850227, -18.426149773}

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