x^2+29x+195=0

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Solution for x^2+29x+195=0 equation: 


Simplifying
x2 + 29x + 195 = 0

Reorder the terms:
195 + 29x + x2 = 0

Solving
195 + 29x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-195' to each side of the equation.
195 + 29x + -195 + x2 = 0 + -195

Reorder the terms:
195 + -195 + 29x + x2 = 0 + -195

Combine like terms: 195 + -195 = 0
0 + 29x + x2 = 0 + -195
29x + x2 = 0 + -195

Combine like terms: 0 + -195 = -195
29x + x2 = -195

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 = -195 + 210.25

Reorder the terms:
210.25 + 29x + x2 = -195 + 210.25

Combine like terms: -195 + 210.25 = 15.25
210.25 + 29x + x2 = 15.25

Factor a perfect square on the left side:
(x + 14.5)(x + 14.5) = 15.25

Calculate the square root of the right side: 3.905124838

Break this problem into two subproblems by setting 
(x + 14.5) equal to 3.905124838 and -3.905124838.


Subproblem 1
x + 14.5 = 3.905124838

Simplifying
x + 14.5 = 3.905124838

Reorder the terms:
14.5 + x = 3.905124838

Solving
14.5 + x = 3.905124838

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 = 3.905124838 + -14.5

Combine like terms: 14.5 + -14.5 = 0.0
0.0 + x = 3.905124838 + -14.5
x = 3.905124838 + -14.5

Combine like terms: 3.905124838 + -14.5 = -10.594875162
x = -10.594875162

Simplifying
x = -10.594875162


Subproblem 2
x + 14.5 = -3.905124838

Simplifying
x + 14.5 = -3.905124838

Reorder the terms:
14.5 + x = -3.905124838

Solving
14.5 + x = -3.905124838

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 = -3.905124838 + -14.5

Combine like terms: 14.5 + -14.5 = 0.0
0.0 + x = -3.905124838 + -14.5
x = -3.905124838 + -14.5

Combine like terms: -3.905124838 + -14.5 = -18.405124838
x = -18.405124838

Simplifying
x = -18.405124838


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-10.594875162, -18.405124838}

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