x^2+8x+16=11+16

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Solution for x^2+8x+16=11+16 equation: 


Simplifying
x2 + 8x + 16 = 11 + 16

Reorder the terms:
16 + 8x + x2 = 11 + 16

Combine like terms: 11 + 16 = 27
16 + 8x + x2 = 27

Solving
16 + 8x + x2 = 27

Solving for variable 'x'.

Reorder the terms:
16 + -27 + 8x + x2 = 27 + -27

Combine like terms: 16 + -27 = -11
-11 + 8x + x2 = 27 + -27

Combine like terms: 27 + -27 = 0
-11 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + 8x + 11 + x2 = 0 + 11

Reorder the terms:
-11 + 11 + 8x + x2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 8x + x2 = 0 + 11
8x + x2 = 0 + 11

Combine like terms: 0 + 11 = 11
8x + x2 = 11

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 11 + 16

Reorder the terms:
16 + 8x + x2 = 11 + 16

Combine like terms: 11 + 16 = 27
16 + 8x + x2 = 27

Factor a perfect square on the left side:
(x + 4)(x + 4) = 27

Calculate the square root of the right side: 5.196152423

Break this problem into two subproblems by setting 
(x + 4) equal to 5.196152423 and -5.196152423.


Subproblem 1
x + 4 = 5.196152423

Simplifying
x + 4 = 5.196152423

Reorder the terms:
4 + x = 5.196152423

Solving
4 + x = 5.196152423

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 5.196152423 + -4

Combine like terms: 4 + -4 = 0
0 + x = 5.196152423 + -4
x = 5.196152423 + -4

Combine like terms: 5.196152423 + -4 = 1.196152423
x = 1.196152423

Simplifying
x = 1.196152423


Subproblem 2
x + 4 = -5.196152423

Simplifying
x + 4 = -5.196152423

Reorder the terms:
4 + x = -5.196152423

Solving
4 + x = -5.196152423

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -5.196152423 + -4

Combine like terms: 4 + -4 = 0
0 + x = -5.196152423 + -4
x = -5.196152423 + -4

Combine like terms: -5.196152423 + -4 = -9.196152423
x = -9.196152423

Simplifying
x = -9.196152423


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.196152423, -9.196152423}

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