x^2+20x+9=0

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Solution for x^2+20x+9=0 equation: 


Simplifying
x2 + 20x + 9 = 0

Reorder the terms:
9 + 20x + x2 = 0

Solving
9 + 20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + 20x + -9 + x2 = 0 + -9

Reorder the terms:
9 + -9 + 20x + x2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 20x + x2 = 0 + -9
20x + x2 = 0 + -9

Combine like terms: 0 + -9 = -9
20x + x2 = -9

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 = -9 + 100

Reorder the terms:
100 + 20x + x2 = -9 + 100

Combine like terms: -9 + 100 = 91
100 + 20x + x2 = 91

Factor a perfect square on the left side:
(x + 10)(x + 10) = 91

Calculate the square root of the right side: 9.539392014

Break this problem into two subproblems by setting 
(x + 10) equal to 9.539392014 and -9.539392014.


Subproblem 1
x + 10 = 9.539392014

Simplifying
x + 10 = 9.539392014

Reorder the terms:
10 + x = 9.539392014

Solving
10 + x = 9.539392014

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 = 9.539392014 + -10

Combine like terms: 10 + -10 = 0
0 + x = 9.539392014 + -10
x = 9.539392014 + -10

Combine like terms: 9.539392014 + -10 = -0.460607986
x = -0.460607986

Simplifying
x = -0.460607986


Subproblem 2
x + 10 = -9.539392014

Simplifying
x + 10 = -9.539392014

Reorder the terms:
10 + x = -9.539392014

Solving
10 + x = -9.539392014

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 = -9.539392014 + -10

Combine like terms: 10 + -10 = 0
0 + x = -9.539392014 + -10
x = -9.539392014 + -10

Combine like terms: -9.539392014 + -10 = -19.539392014
x = -19.539392014

Simplifying
x = -19.539392014


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.460607986, -19.539392014}

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