x=-x^2-10x-25

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Solution for x=-x^2-10x-25 equation: 


Simplifying
x = -1x2 + -10x + -25

Reorder the terms:
x = -25 + -10x + -1x2

Solving
x = -25 + -10x + -1x2

Solving for variable 'x'.

Reorder the terms:
25 + x + 10x + x2 = -25 + -10x + -1x2 + 25 + 10x + x2

Combine like terms: x + 10x = 11x
25 + 11x + x2 = -25 + -10x + -1x2 + 25 + 10x + x2

Reorder the terms:
25 + 11x + x2 = -25 + 25 + -10x + 10x + -1x2 + x2

Combine like terms: -25 + 25 = 0
25 + 11x + x2 = 0 + -10x + 10x + -1x2 + x2
25 + 11x + x2 = -10x + 10x + -1x2 + x2

Combine like terms: -10x + 10x = 0
25 + 11x + x2 = 0 + -1x2 + x2
25 + 11x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
25 + 11x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-25' to each side of the equation.
25 + 11x + -25 + x2 = 0 + -25

Reorder the terms:
25 + -25 + 11x + x2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + 11x + x2 = 0 + -25
11x + x2 = 0 + -25

Combine like terms: 0 + -25 = -25
11x + x2 = -25

The x term is 11x.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11x + 30.25 + x2 = -25 + 30.25

Reorder the terms:
30.25 + 11x + x2 = -25 + 30.25

Combine like terms: -25 + 30.25 = 5.25
30.25 + 11x + x2 = 5.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(x + 5.5) equal to 2.291287847 and -2.291287847.


Subproblem 1
x + 5.5 = 2.291287847

Simplifying
x + 5.5 = 2.291287847

Reorder the terms:
5.5 + x = 2.291287847

Solving
5.5 + x = 2.291287847

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = 2.291287847 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = 2.291287847 + -5.5
x = 2.291287847 + -5.5

Combine like terms: 2.291287847 + -5.5 = -3.208712153
x = -3.208712153

Simplifying
x = -3.208712153


Subproblem 2
x + 5.5 = -2.291287847

Simplifying
x + 5.5 = -2.291287847

Reorder the terms:
5.5 + x = -2.291287847

Solving
5.5 + x = -2.291287847

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = -2.291287847 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = -2.291287847 + -5.5
x = -2.291287847 + -5.5

Combine like terms: -2.291287847 + -5.5 = -7.791287847
x = -7.791287847

Simplifying
x = -7.791287847


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.208712153, -7.791287847}

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