x^2+11x+10=x

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Solution for x^2+11x+10=x equation: 


Simplifying
x2 + 11x + 10 = x

Reorder the terms:
10 + 11x + x2 = x

Solving
10 + 11x + x2 = x

Solving for variable 'x'.

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

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

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

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = -10 + 25

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

Combine like terms: -10 + 25 = 15
25 + 10x + x2 = 15

Factor a perfect square on the left side:
(x + 5)(x + 5) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(x + 5) equal to 3.872983346 and -3.872983346.


Subproblem 1
x + 5 = 3.872983346

Simplifying
x + 5 = 3.872983346

Reorder the terms:
5 + x = 3.872983346

Solving
5 + x = 3.872983346

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 = 3.872983346 + -5

Combine like terms: 5 + -5 = 0
0 + x = 3.872983346 + -5
x = 3.872983346 + -5

Combine like terms: 3.872983346 + -5 = -1.127016654
x = -1.127016654

Simplifying
x = -1.127016654


Subproblem 2
x + 5 = -3.872983346

Simplifying
x + 5 = -3.872983346

Reorder the terms:
5 + x = -3.872983346

Solving
5 + x = -3.872983346

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 = -3.872983346 + -5

Combine like terms: 5 + -5 = 0
0 + x = -3.872983346 + -5
x = -3.872983346 + -5

Combine like terms: -3.872983346 + -5 = -8.872983346
x = -8.872983346

Simplifying
x = -8.872983346


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.127016654, -8.872983346}

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