x^2+5.333x+5=0

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Solution for x^2+5.333x+5=0 equation: 


Simplifying
x2 + 5.333x + 5 = 0

Reorder the terms:
5 + 5.333x + x2 = 0

Solving
5 + 5.333x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 5.333x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + 5.333x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 5.333x + x2 = 0 + -5
5.333x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
5.333x + x2 = -5

The x term is 5.333x.  Take half its coefficient (2.6665).
Square it (7.11022225) and add it to both sides.

Add '7.11022225' to each side of the equation.
5.333x + 7.11022225 + x2 = -5 + 7.11022225

Reorder the terms:
7.11022225 + 5.333x + x2 = -5 + 7.11022225

Combine like terms: -5 + 7.11022225 = 2.11022225
7.11022225 + 5.333x + x2 = 2.11022225

Factor a perfect square on the left side:
(x + 2.6665)(x + 2.6665) = 2.11022225

Calculate the square root of the right side: 1.452660404

Break this problem into two subproblems by setting 
(x + 2.6665) equal to 1.452660404 and -1.452660404.


Subproblem 1
x + 2.6665 = 1.452660404

Simplifying
x + 2.6665 = 1.452660404

Reorder the terms:
2.6665 + x = 1.452660404

Solving
2.6665 + x = 1.452660404

Solving for variable 'x'.

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

Add '-2.6665' to each side of the equation.
2.6665 + -2.6665 + x = 1.452660404 + -2.6665

Combine like terms: 2.6665 + -2.6665 = 0.0000
0.0000 + x = 1.452660404 + -2.6665
x = 1.452660404 + -2.6665

Combine like terms: 1.452660404 + -2.6665 = -1.213839596
x = -1.213839596

Simplifying
x = -1.213839596


Subproblem 2
x + 2.6665 = -1.452660404

Simplifying
x + 2.6665 = -1.452660404

Reorder the terms:
2.6665 + x = -1.452660404

Solving
2.6665 + x = -1.452660404

Solving for variable 'x'.

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

Add '-2.6665' to each side of the equation.
2.6665 + -2.6665 + x = -1.452660404 + -2.6665

Combine like terms: 2.6665 + -2.6665 = 0.0000
0.0000 + x = -1.452660404 + -2.6665
x = -1.452660404 + -2.6665

Combine like terms: -1.452660404 + -2.6665 = -4.119160404
x = -4.119160404

Simplifying
x = -4.119160404


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.213839596, -4.119160404}

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