(x+3)(x+3)=1.16666666667

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Solution for (x+3)(x+3)=1.16666666667 equation: 


Simplifying
(x + 3)(x + 3) = 1.16666666667

Reorder the terms:
(3 + x)(x + 3) = 1.16666666667

Reorder the terms:
(3 + x)(3 + x) = 1.16666666667

Multiply (3 + x) * (3 + x)
(3(3 + x) + x(3 + x)) = 1.16666666667
((3 * 3 + x * 3) + x(3 + x)) = 1.16666666667
((9 + 3x) + x(3 + x)) = 1.16666666667
(9 + 3x + (3 * x + x * x)) = 1.16666666667
(9 + 3x + (3x + x2)) = 1.16666666667

Combine like terms: 3x + 3x = 6x
(9 + 6x + x2) = 1.16666666667

Solving
9 + 6x + x2 = 1.16666666667

Solving for variable 'x'.

Reorder the terms:
9 + -1.16666666667 + 6x + x2 = 1.16666666667 + -1.16666666667

Combine like terms: 9 + -1.16666666667 = 7.83333333333
7.83333333333 + 6x + x2 = 1.16666666667 + -1.16666666667

Combine like terms: 1.16666666667 + -1.16666666667 = 0.00000000000
7.83333333333 + 6x + x2 = 0.00000000000

Begin completing the square.

Move the constant term to the right:

Add '-7.83333333333' to each side of the equation.
7.83333333333 + 6x + -7.83333333333 + x2 = 0.00000000000 + -7.83333333333

Reorder the terms:
7.83333333333 + -7.83333333333 + 6x + x2 = 0.00000000000 + -7.83333333333

Combine like terms: 7.83333333333 + -7.83333333333 = 0.00000000000
0.00000000000 + 6x + x2 = 0.00000000000 + -7.83333333333
6x + x2 = 0.00000000000 + -7.83333333333

Combine like terms: 0.00000000000 + -7.83333333333 = -7.83333333333
6x + x2 = -7.83333333333

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = -7.83333333333 + 9

Reorder the terms:
9 + 6x + x2 = -7.83333333333 + 9

Combine like terms: -7.83333333333 + 9 = 1.16666666667
9 + 6x + x2 = 1.16666666667

Factor a perfect square on the left side:
(x + 3)(x + 3) = 1.16666666667

Calculate the square root of the right side: 1.08012345

Break this problem into two subproblems by setting 
(x + 3) equal to 1.08012345 and -1.08012345.


Subproblem 1
x + 3 = 1.08012345

Simplifying
x + 3 = 1.08012345

Reorder the terms:
3 + x = 1.08012345

Solving
3 + x = 1.08012345

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 1.08012345 + -3

Combine like terms: 3 + -3 = 0
0 + x = 1.08012345 + -3
x = 1.08012345 + -3

Combine like terms: 1.08012345 + -3 = -1.91987655
x = -1.91987655

Simplifying
x = -1.91987655


Subproblem 2
x + 3 = -1.08012345

Simplifying
x + 3 = -1.08012345

Reorder the terms:
3 + x = -1.08012345

Solving
3 + x = -1.08012345

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -1.08012345 + -3

Combine like terms: 3 + -3 = 0
0 + x = -1.08012345 + -3
x = -1.08012345 + -3

Combine like terms: -1.08012345 + -3 = -4.08012345
x = -4.08012345

Simplifying
x = -4.08012345


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.91987655, -4.08012345}

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