x^2+20x+8=0

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Solution for x^2+20x+8=0 equation: 


Simplifying
x2 + 20x + 8 = 0

Reorder the terms:
8 + 20x + x2 = 0

Solving
8 + 20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + 20x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + 20x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 20x + x2 = 0 + -8
20x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
20x + x2 = -8

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 = -8 + 100

Reorder the terms:
100 + 20x + x2 = -8 + 100

Combine like terms: -8 + 100 = 92
100 + 20x + x2 = 92

Factor a perfect square on the left side:
(x + 10)(x + 10) = 92

Calculate the square root of the right side: 9.591663047

Break this problem into two subproblems by setting 
(x + 10) equal to 9.591663047 and -9.591663047.


Subproblem 1
x + 10 = 9.591663047

Simplifying
x + 10 = 9.591663047

Reorder the terms:
10 + x = 9.591663047

Solving
10 + x = 9.591663047

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 = 9.591663047 + -10

Combine like terms: 10 + -10 = 0
0 + x = 9.591663047 + -10
x = 9.591663047 + -10

Combine like terms: 9.591663047 + -10 = -0.408336953
x = -0.408336953

Simplifying
x = -0.408336953


Subproblem 2
x + 10 = -9.591663047

Simplifying
x + 10 = -9.591663047

Reorder the terms:
10 + x = -9.591663047

Solving
10 + x = -9.591663047

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 = -9.591663047 + -10

Combine like terms: 10 + -10 = 0
0 + x = -9.591663047 + -10
x = -9.591663047 + -10

Combine like terms: -9.591663047 + -10 = -19.591663047
x = -19.591663047

Simplifying
x = -19.591663047


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.408336953, -19.591663047}

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