6*(x+2)*(x+2)-5=0

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Solution for 6*(x+2)*(x+2)-5=0 equation: 


Simplifying
6(x + 2)(x + 2) + -5 = 0

Reorder the terms:
6(2 + x)(x + 2) + -5 = 0

Reorder the terms:
6(2 + x)(2 + x) + -5 = 0

Multiply (2 + x) * (2 + x)
6(2(2 + x) + x(2 + x)) + -5 = 0
6((2 * 2 + x * 2) + x(2 + x)) + -5 = 0
6((4 + 2x) + x(2 + x)) + -5 = 0
6(4 + 2x + (2 * x + x * x)) + -5 = 0
6(4 + 2x + (2x + x2)) + -5 = 0

Combine like terms: 2x + 2x = 4x
6(4 + 4x + x2) + -5 = 0
(4 * 6 + 4x * 6 + x2 * 6) + -5 = 0
(24 + 24x + 6x2) + -5 = 0

Reorder the terms:
24 + -5 + 24x + 6x2 = 0

Combine like terms: 24 + -5 = 19
19 + 24x + 6x2 = 0

Solving
19 + 24x + 6x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
6 the coefficient of the squared term: 

Divide each side by '6'.
3.166666667 + 4x + x2 = 0

Move the constant term to the right:

Add '-3.166666667' to each side of the equation.
3.166666667 + 4x + -3.166666667 + x2 = 0 + -3.166666667

Reorder the terms:
3.166666667 + -3.166666667 + 4x + x2 = 0 + -3.166666667

Combine like terms: 3.166666667 + -3.166666667 = 0.000000000
0.000000000 + 4x + x2 = 0 + -3.166666667
4x + x2 = 0 + -3.166666667

Combine like terms: 0 + -3.166666667 = -3.166666667
4x + x2 = -3.166666667

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = -3.166666667 + 4

Reorder the terms:
4 + 4x + x2 = -3.166666667 + 4

Combine like terms: -3.166666667 + 4 = 0.833333333
4 + 4x + x2 = 0.833333333

Factor a perfect square on the left side:
(x + 2)(x + 2) = 0.833333333

Calculate the square root of the right side: 0.912870929

Break this problem into two subproblems by setting 
(x + 2) equal to 0.912870929 and -0.912870929.


Subproblem 1
x + 2 = 0.912870929

Simplifying
x + 2 = 0.912870929

Reorder the terms:
2 + x = 0.912870929

Solving
2 + x = 0.912870929

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 0.912870929 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0.912870929 + -2
x = 0.912870929 + -2

Combine like terms: 0.912870929 + -2 = -1.087129071
x = -1.087129071

Simplifying
x = -1.087129071


Subproblem 2
x + 2 = -0.912870929

Simplifying
x + 2 = -0.912870929

Reorder the terms:
2 + x = -0.912870929

Solving
2 + x = -0.912870929

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -0.912870929 + -2

Combine like terms: 2 + -2 = 0
0 + x = -0.912870929 + -2
x = -0.912870929 + -2

Combine like terms: -0.912870929 + -2 = -2.912870929
x = -2.912870929

Simplifying
x = -2.912870929


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.087129071, -2.912870929}

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