x^2+10x+11=0

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Solution for x^2+10x+11=0 equation: 


Simplifying
x2 + 10x + 11 = 0

Reorder the terms:
11 + 10x + x2 = 0

Solving
11 + 10x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + 10x + -11 + x2 = 0 + -11

Reorder the terms:
11 + -11 + 10x + x2 = 0 + -11

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

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

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 = -11 + 25

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

Combine like terms: -11 + 25 = 14
25 + 10x + x2 = 14

Factor a perfect square on the left side:
(x + 5)(x + 5) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(x + 5) equal to 3.741657387 and -3.741657387.


Subproblem 1
x + 5 = 3.741657387

Simplifying
x + 5 = 3.741657387

Reorder the terms:
5 + x = 3.741657387

Solving
5 + x = 3.741657387

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 = 3.741657387 + -5

Combine like terms: 5 + -5 = 0
0 + x = 3.741657387 + -5
x = 3.741657387 + -5

Combine like terms: 3.741657387 + -5 = -1.258342613
x = -1.258342613

Simplifying
x = -1.258342613


Subproblem 2
x + 5 = -3.741657387

Simplifying
x + 5 = -3.741657387

Reorder the terms:
5 + x = -3.741657387

Solving
5 + x = -3.741657387

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 = -3.741657387 + -5

Combine like terms: 5 + -5 = 0
0 + x = -3.741657387 + -5
x = -3.741657387 + -5

Combine like terms: -3.741657387 + -5 = -8.741657387
x = -8.741657387

Simplifying
x = -8.741657387


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.258342613, -8.741657387}

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