(x+12)(x+12)=360

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Solution for (x+12)(x+12)=360 equation:


Simplifying
(x + 12)(x + 12) = 360

Reorder the terms:
(12 + x)(x + 12) = 360

Reorder the terms:
(12 + x)(12 + x) = 360

Multiply (12 + x) * (12 + x)
(12(12 + x) + x(12 + x)) = 360
((12 * 12 + x * 12) + x(12 + x)) = 360
((144 + 12x) + x(12 + x)) = 360
(144 + 12x + (12 * x + x * x)) = 360
(144 + 12x + (12x + x2)) = 360

Combine like terms: 12x + 12x = 24x
(144 + 24x + x2) = 360

Solving
144 + 24x + x2 = 360

Solving for variable 'x'.

Reorder the terms:
144 + -360 + 24x + x2 = 360 + -360

Combine like terms: 144 + -360 = -216
-216 + 24x + x2 = 360 + -360

Combine like terms: 360 + -360 = 0
-216 + 24x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '216' to each side of the equation.
-216 + 24x + 216 + x2 = 0 + 216

Reorder the terms:
-216 + 216 + 24x + x2 = 0 + 216

Combine like terms: -216 + 216 = 0
0 + 24x + x2 = 0 + 216
24x + x2 = 0 + 216

Combine like terms: 0 + 216 = 216
24x + x2 = 216

The x term is 24x.  Take half its coefficient (12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
24x + 144 + x2 = 216 + 144

Reorder the terms:
144 + 24x + x2 = 216 + 144

Combine like terms: 216 + 144 = 360
144 + 24x + x2 = 360

Factor a perfect square on the left side:
(x + 12)(x + 12) = 360

Calculate the square root of the right side: 18.973665961

Break this problem into two subproblems by setting 
(x + 12) equal to 18.973665961 and -18.973665961.


Subproblem 1
x + 12 = 18.973665961

Simplifying
x + 12 = 18.973665961

Reorder the terms:
12 + x = 18.973665961

Solving
12 + x = 18.973665961

Solving for variable 'x'.

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

Add '-12' to each side of the equation.
12 + -12 + x = 18.973665961 + -12

Combine like terms: 12 + -12 = 0
0 + x = 18.973665961 + -12
x = 18.973665961 + -12

Combine like terms: 18.973665961 + -12 = 6.973665961
x = 6.973665961

Simplifying
x = 6.973665961


Subproblem 2
x + 12 = -18.973665961

Simplifying
x + 12 = -18.973665961

Reorder the terms:
12 + x = -18.973665961

Solving
12 + x = -18.973665961

Solving for variable 'x'.

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

Add '-12' to each side of the equation.
12 + -12 + x = -18.973665961 + -12

Combine like terms: 12 + -12 = 0
0 + x = -18.973665961 + -12
x = -18.973665961 + -12

Combine like terms: -18.973665961 + -12 = -30.973665961
x = -30.973665961

Simplifying
x = -30.973665961


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.973665961, -30.973665961}

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