x^2+8x+16=1.777777778

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Solution for x^2+8x+16=1.777777778 equation: 


Simplifying
x2 + 8x + 16 = 1.777777778

Reorder the terms:
16 + 8x + x2 = 1.777777778

Solving
16 + 8x + x2 = 1.777777778

Solving for variable 'x'.

Reorder the terms:
16 + -1.777777778 + 8x + x2 = 1.777777778 + -1.777777778

Combine like terms: 16 + -1.777777778 = 14.222222222
14.222222222 + 8x + x2 = 1.777777778 + -1.777777778

Combine like terms: 1.777777778 + -1.777777778 = 0.000000000
14.222222222 + 8x + x2 = 0.000000000

Begin completing the square.

Move the constant term to the right:

Add '-14.222222222' to each side of the equation.
14.222222222 + 8x + -14.222222222 + x2 = 0.000000000 + -14.222222222

Reorder the terms:
14.222222222 + -14.222222222 + 8x + x2 = 0.000000000 + -14.222222222

Combine like terms: 14.222222222 + -14.222222222 = 0.000000000
0.000000000 + 8x + x2 = 0.000000000 + -14.222222222
8x + x2 = 0.000000000 + -14.222222222

Combine like terms: 0.000000000 + -14.222222222 = -14.222222222
8x + x2 = -14.222222222

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 = -14.222222222 + 16

Reorder the terms:
16 + 8x + x2 = -14.222222222 + 16

Combine like terms: -14.222222222 + 16 = 1.777777778
16 + 8x + x2 = 1.777777778

Factor a perfect square on the left side:
(x + 4)(x + 4) = 1.777777778

Calculate the square root of the right side: 1.333333333

Break this problem into two subproblems by setting 
(x + 4) equal to 1.333333333 and -1.333333333.


Subproblem 1
x + 4 = 1.333333333

Simplifying
x + 4 = 1.333333333

Reorder the terms:
4 + x = 1.333333333

Solving
4 + x = 1.333333333

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 = 1.333333333 + -4

Combine like terms: 4 + -4 = 0
0 + x = 1.333333333 + -4
x = 1.333333333 + -4

Combine like terms: 1.333333333 + -4 = -2.666666667
x = -2.666666667

Simplifying
x = -2.666666667


Subproblem 2
x + 4 = -1.333333333

Simplifying
x + 4 = -1.333333333

Reorder the terms:
4 + x = -1.333333333

Solving
4 + x = -1.333333333

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 = -1.333333333 + -4

Combine like terms: 4 + -4 = 0
0 + x = -1.333333333 + -4
x = -1.333333333 + -4

Combine like terms: -1.333333333 + -4 = -5.333333333
x = -5.333333333

Simplifying
x = -5.333333333


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.666666667, -5.333333333}

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