x^2+29x+19=0

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Solution for x^2+29x+19=0 equation: 


Simplifying
x2 + 29x + 19 = 0

Reorder the terms:
19 + 29x + x2 = 0

Solving
19 + 29x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-19' to each side of the equation.
19 + 29x + -19 + x2 = 0 + -19

Reorder the terms:
19 + -19 + 29x + x2 = 0 + -19

Combine like terms: 19 + -19 = 0
0 + 29x + x2 = 0 + -19
29x + x2 = 0 + -19

Combine like terms: 0 + -19 = -19
29x + x2 = -19

The x term is 29x.  Take half its coefficient (14.5).
Square it (210.25) and add it to both sides.

Add '210.25' to each side of the equation.
29x + 210.25 + x2 = -19 + 210.25

Reorder the terms:
210.25 + 29x + x2 = -19 + 210.25

Combine like terms: -19 + 210.25 = 191.25
210.25 + 29x + x2 = 191.25

Factor a perfect square on the left side:
(x + 14.5)(x + 14.5) = 191.25

Calculate the square root of the right side: 13.829316686

Break this problem into two subproblems by setting 
(x + 14.5) equal to 13.829316686 and -13.829316686.


Subproblem 1
x + 14.5 = 13.829316686

Simplifying
x + 14.5 = 13.829316686

Reorder the terms:
14.5 + x = 13.829316686

Solving
14.5 + x = 13.829316686

Solving for variable 'x'.

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

Add '-14.5' to each side of the equation.
14.5 + -14.5 + x = 13.829316686 + -14.5

Combine like terms: 14.5 + -14.5 = 0.0
0.0 + x = 13.829316686 + -14.5
x = 13.829316686 + -14.5

Combine like terms: 13.829316686 + -14.5 = -0.670683314
x = -0.670683314

Simplifying
x = -0.670683314


Subproblem 2
x + 14.5 = -13.829316686

Simplifying
x + 14.5 = -13.829316686

Reorder the terms:
14.5 + x = -13.829316686

Solving
14.5 + x = -13.829316686

Solving for variable 'x'.

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

Add '-14.5' to each side of the equation.
14.5 + -14.5 + x = -13.829316686 + -14.5

Combine like terms: 14.5 + -14.5 = 0.0
0.0 + x = -13.829316686 + -14.5
x = -13.829316686 + -14.5

Combine like terms: -13.829316686 + -14.5 = -28.329316686
x = -28.329316686

Simplifying
x = -28.329316686


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.670683314, -28.329316686}

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