(6+x)(6+x)=146

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Solution for (6+x)(6+x)=146 equation: 


Simplifying
(6 + x)(6 + x) = 146

Multiply (6 + x) * (6 + x)
(6(6 + x) + x(6 + x)) = 146
((6 * 6 + x * 6) + x(6 + x)) = 146
((36 + 6x) + x(6 + x)) = 146
(36 + 6x + (6 * x + x * x)) = 146
(36 + 6x + (6x + x2)) = 146

Combine like terms: 6x + 6x = 12x
(36 + 12x + x2) = 146

Solving
36 + 12x + x2 = 146

Solving for variable 'x'.

Reorder the terms:
36 + -146 + 12x + x2 = 146 + -146

Combine like terms: 36 + -146 = -110
-110 + 12x + x2 = 146 + -146

Combine like terms: 146 + -146 = 0
-110 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '110' to each side of the equation.
-110 + 12x + 110 + x2 = 0 + 110

Reorder the terms:
-110 + 110 + 12x + x2 = 0 + 110

Combine like terms: -110 + 110 = 0
0 + 12x + x2 = 0 + 110
12x + x2 = 0 + 110

Combine like terms: 0 + 110 = 110
12x + x2 = 110

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = 110 + 36

Reorder the terms:
36 + 12x + x2 = 110 + 36

Combine like terms: 110 + 36 = 146
36 + 12x + x2 = 146

Factor a perfect square on the left side:
(x + 6)(x + 6) = 146

Calculate the square root of the right side: 12.083045974

Break this problem into two subproblems by setting 
(x + 6) equal to 12.083045974 and -12.083045974.


Subproblem 1
x + 6 = 12.083045974

Simplifying
x + 6 = 12.083045974

Reorder the terms:
6 + x = 12.083045974

Solving
6 + x = 12.083045974

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = 12.083045974 + -6

Combine like terms: 6 + -6 = 0
0 + x = 12.083045974 + -6
x = 12.083045974 + -6

Combine like terms: 12.083045974 + -6 = 6.083045974
x = 6.083045974

Simplifying
x = 6.083045974


Subproblem 2
x + 6 = -12.083045974

Simplifying
x + 6 = -12.083045974

Reorder the terms:
6 + x = -12.083045974

Solving
6 + x = -12.083045974

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = -12.083045974 + -6

Combine like terms: 6 + -6 = 0
0 + x = -12.083045974 + -6
x = -12.083045974 + -6

Combine like terms: -12.083045974 + -6 = -18.083045974
x = -18.083045974

Simplifying
x = -18.083045974


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.083045974, -18.083045974}

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