x^2+8x+16=1.77778

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Solution for x^2+8x+16=1.77778 equation: 


Simplifying
x2 + 8x + 16 = 1.77778

Reorder the terms:
16 + 8x + x2 = 1.77778

Solving
16 + 8x + x2 = 1.77778

Solving for variable 'x'.

Reorder the terms:
16 + -1.77778 + 8x + x2 = 1.77778 + -1.77778

Combine like terms: 16 + -1.77778 = 14.22222
14.22222 + 8x + x2 = 1.77778 + -1.77778

Combine like terms: 1.77778 + -1.77778 = 0.00000
14.22222 + 8x + x2 = 0.00000

Begin completing the square.

Move the constant term to the right:

Add '-14.22222' to each side of the equation.
14.22222 + 8x + -14.22222 + x2 = 0.00000 + -14.22222

Reorder the terms:
14.22222 + -14.22222 + 8x + x2 = 0.00000 + -14.22222

Combine like terms: 14.22222 + -14.22222 = 0.00000
0.00000 + 8x + x2 = 0.00000 + -14.22222
8x + x2 = 0.00000 + -14.22222

Combine like terms: 0.00000 + -14.22222 = -14.22222
8x + x2 = -14.22222

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 = -14.22222 + 16

Reorder the terms:
16 + 8x + x2 = -14.22222 + 16

Combine like terms: -14.22222 + 16 = 1.77778
16 + 8x + x2 = 1.77778

Factor a perfect square on the left side:
(x + 4)(x + 4) = 1.77778

Calculate the square root of the right side: 1.333334167

Break this problem into two subproblems by setting 
(x + 4) equal to 1.333334167 and -1.333334167.


Subproblem 1
x + 4 = 1.333334167

Simplifying
x + 4 = 1.333334167

Reorder the terms:
4 + x = 1.333334167

Solving
4 + x = 1.333334167

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 = 1.333334167 + -4

Combine like terms: 4 + -4 = 0
0 + x = 1.333334167 + -4
x = 1.333334167 + -4

Combine like terms: 1.333334167 + -4 = -2.666665833
x = -2.666665833

Simplifying
x = -2.666665833


Subproblem 2
x + 4 = -1.333334167

Simplifying
x + 4 = -1.333334167

Reorder the terms:
4 + x = -1.333334167

Solving
4 + x = -1.333334167

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 = -1.333334167 + -4

Combine like terms: 4 + -4 = 0
0 + x = -1.333334167 + -4
x = -1.333334167 + -4

Combine like terms: -1.333334167 + -4 = -5.333334167
x = -5.333334167

Simplifying
x = -5.333334167


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.666665833, -5.333334167}

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