-x^2-20x-53=0

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Solution for -x^2-20x-53=0 equation: 


Simplifying
-1x2 + -20x + -53 = 0

Reorder the terms:
-53 + -20x + -1x2 = 0

Solving
-53 + -20x + -1x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(53 + 20x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(53 + 20x + x2)' equal to zero and attempt to solve:

Simplifying
53 + 20x + x2 = 0

Solving
53 + 20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-53' to each side of the equation.
53 + 20x + -53 + x2 = 0 + -53

Reorder the terms:
53 + -53 + 20x + x2 = 0 + -53

Combine like terms: 53 + -53 = 0
0 + 20x + x2 = 0 + -53
20x + x2 = 0 + -53

Combine like terms: 0 + -53 = -53
20x + x2 = -53

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 = -53 + 100

Reorder the terms:
100 + 20x + x2 = -53 + 100

Combine like terms: -53 + 100 = 47
100 + 20x + x2 = 47

Factor a perfect square on the left side:
(x + 10)(x + 10) = 47

Calculate the square root of the right side: 6.8556546

Break this problem into two subproblems by setting 
(x + 10) equal to 6.8556546 and -6.8556546.


Subproblem 1
x + 10 = 6.8556546

Simplifying
x + 10 = 6.8556546

Reorder the terms:
10 + x = 6.8556546

Solving
10 + x = 6.8556546

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 = 6.8556546 + -10

Combine like terms: 10 + -10 = 0
0 + x = 6.8556546 + -10
x = 6.8556546 + -10

Combine like terms: 6.8556546 + -10 = -3.1443454
x = -3.1443454

Simplifying
x = -3.1443454


Subproblem 2
x + 10 = -6.8556546

Simplifying
x + 10 = -6.8556546

Reorder the terms:
10 + x = -6.8556546

Solving
10 + x = -6.8556546

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 = -6.8556546 + -10

Combine like terms: 10 + -10 = 0
0 + x = -6.8556546 + -10
x = -6.8556546 + -10

Combine like terms: -6.8556546 + -10 = -16.8556546
x = -16.8556546

Simplifying
x = -16.8556546


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.1443454, -16.8556546}
Solution
x = {-3.1443454, -16.8556546}

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