x^2+10x+25=11

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Solution for x^2+10x+25=11 equation: 


Simplifying
x2 + 10x + 25 = 11

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

Solving
25 + 10x + x2 = 11

Solving for variable 'x'.

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

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

Combine like terms: 11 + -11 = 0
14 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-14' to each side of the equation.
14 + 10x + -14 + x2 = 0 + -14

Reorder the terms:
14 + -14 + 10x + x2 = 0 + -14

Combine like terms: 14 + -14 = 0
0 + 10x + x2 = 0 + -14
10x + x2 = 0 + -14

Combine like terms: 0 + -14 = -14
10x + x2 = -14

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 = -14 + 25

Reorder the terms:
25 + 10x + x2 = -14 + 25

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

Factor a perfect square on the left side:
(x + 5)(x + 5) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(x + 5) equal to 3.31662479 and -3.31662479.


Subproblem 1
x + 5 = 3.31662479

Simplifying
x + 5 = 3.31662479

Reorder the terms:
5 + x = 3.31662479

Solving
5 + x = 3.31662479

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 = 3.31662479 + -5

Combine like terms: 5 + -5 = 0
0 + x = 3.31662479 + -5
x = 3.31662479 + -5

Combine like terms: 3.31662479 + -5 = -1.68337521
x = -1.68337521

Simplifying
x = -1.68337521


Subproblem 2
x + 5 = -3.31662479

Simplifying
x + 5 = -3.31662479

Reorder the terms:
5 + x = -3.31662479

Solving
5 + x = -3.31662479

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 = -3.31662479 + -5

Combine like terms: 5 + -5 = 0
0 + x = -3.31662479 + -5
x = -3.31662479 + -5

Combine like terms: -3.31662479 + -5 = -8.31662479
x = -8.31662479

Simplifying
x = -8.31662479


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.68337521, -8.31662479}

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