-x^2-20x-5=0

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Solution for -x^2-20x-5=0 equation: 


Simplifying
-1x2 + -20x + -5 = 0

Reorder the terms:
-5 + -20x + -1x2 = 0

Solving
-5 + -20x + -1x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 20x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(5 + 20x + x2)' equal to zero and attempt to solve:

Simplifying
5 + 20x + x2 = 0

Solving
5 + 20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 20x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + 20x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 20x + x2 = 0 + -5
20x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
20x + x2 = -5

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 = -5 + 100

Reorder the terms:
100 + 20x + x2 = -5 + 100

Combine like terms: -5 + 100 = 95
100 + 20x + x2 = 95

Factor a perfect square on the left side:
(x + 10)(x + 10) = 95

Calculate the square root of the right side: 9.746794345

Break this problem into two subproblems by setting 
(x + 10) equal to 9.746794345 and -9.746794345.


Subproblem 1
x + 10 = 9.746794345

Simplifying
x + 10 = 9.746794345

Reorder the terms:
10 + x = 9.746794345

Solving
10 + x = 9.746794345

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 = 9.746794345 + -10

Combine like terms: 10 + -10 = 0
0 + x = 9.746794345 + -10
x = 9.746794345 + -10

Combine like terms: 9.746794345 + -10 = -0.253205655
x = -0.253205655

Simplifying
x = -0.253205655


Subproblem 2
x + 10 = -9.746794345

Simplifying
x + 10 = -9.746794345

Reorder the terms:
10 + x = -9.746794345

Solving
10 + x = -9.746794345

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 = -9.746794345 + -10

Combine like terms: 10 + -10 = 0
0 + x = -9.746794345 + -10
x = -9.746794345 + -10

Combine like terms: -9.746794345 + -10 = -19.746794345
x = -19.746794345

Simplifying
x = -19.746794345


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.253205655, -19.746794345}
Solution
x = {-0.253205655, -19.746794345}

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