-x^2-10x-2=0

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Solution for -x^2-10x-2=0 equation: 


Simplifying
-1x2 + -10x + -2 = 0

Reorder the terms:
-2 + -10x + -1x2 = 0

Solving
-2 + -10x + -1x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(2 + 10x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(2 + 10x + x2)' equal to zero and attempt to solve:

Simplifying
2 + 10x + x2 = 0

Solving
2 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 10x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + 10x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 10x + x2 = 0 + -2
10x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
10x + x2 = -2

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = -2 + 25

Reorder the terms:
25 + 10x + x2 = -2 + 25

Combine like terms: -2 + 25 = 23
25 + 10x + x2 = 23

Factor a perfect square on the left side:
(x + 5)(x + 5) = 23

Calculate the square root of the right side: 4.795831523

Break this problem into two subproblems by setting 
(x + 5) equal to 4.795831523 and -4.795831523.


Subproblem 1
x + 5 = 4.795831523

Simplifying
x + 5 = 4.795831523

Reorder the terms:
5 + x = 4.795831523

Solving
5 + x = 4.795831523

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + x = 4.795831523 + -5

Combine like terms: 5 + -5 = 0
0 + x = 4.795831523 + -5
x = 4.795831523 + -5

Combine like terms: 4.795831523 + -5 = -0.204168477
x = -0.204168477

Simplifying
x = -0.204168477


Subproblem 2
x + 5 = -4.795831523

Simplifying
x + 5 = -4.795831523

Reorder the terms:
5 + x = -4.795831523

Solving
5 + x = -4.795831523

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + x = -4.795831523 + -5

Combine like terms: 5 + -5 = 0
0 + x = -4.795831523 + -5
x = -4.795831523 + -5

Combine like terms: -4.795831523 + -5 = -9.795831523
x = -9.795831523

Simplifying
x = -9.795831523


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.204168477, -9.795831523}
Solution
x = {-0.204168477, -9.795831523}

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