(2x*2x)+(x+5)*(x+5)=(3x+12)*(3x+12)

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Solution for (2x*2x)+(x+5)*(x+5)=(3x+12)*(3x+12) equation: 


Simplifying
(2x * 2x) + (x + 5)(x + 5) = (3x + 12)(3x + 12)

Reorder the terms for easier multiplication:
(2 * 2x * x) + (x + 5)(x + 5) = (3x + 12)(3x + 12)

Multiply 2 * 2
(4x * x) + (x + 5)(x + 5) = (3x + 12)(3x + 12)

Multiply x * x
(4x2) + (x + 5)(x + 5) = (3x + 12)(3x + 12)

Reorder the terms:
(4x2) + (5 + x)(x + 5) = (3x + 12)(3x + 12)

Reorder the terms:
(4x2) + (5 + x)(5 + x) = (3x + 12)(3x + 12)

Multiply (5 + x) * (5 + x)
(4x2) + (5(5 + x) + x(5 + x)) = (3x + 12)(3x + 12)
(4x2) + ((5 * 5 + x * 5) + x(5 + x)) = (3x + 12)(3x + 12)
(4x2) + ((25 + 5x) + x(5 + x)) = (3x + 12)(3x + 12)
(4x2) + (25 + 5x + (5 * x + x * x)) = (3x + 12)(3x + 12)
(4x2) + (25 + 5x + (5x + x2)) = (3x + 12)(3x + 12)

Combine like terms: 5x + 5x = 10x
(4x2) + (25 + 10x + x2) = (3x + 12)(3x + 12)

Reorder the terms:
25 + 10x + (4x2) + x2 = (3x + 12)(3x + 12)

Combine like terms: (4x2) + x2 = 5x2
25 + 10x + 5x2 = (3x + 12)(3x + 12)

Reorder the terms:
25 + 10x + 5x2 = (12 + 3x)(3x + 12)

Reorder the terms:
25 + 10x + 5x2 = (12 + 3x)(12 + 3x)

Multiply (12 + 3x) * (12 + 3x)
25 + 10x + 5x2 = (12(12 + 3x) + 3x * (12 + 3x))
25 + 10x + 5x2 = ((12 * 12 + 3x * 12) + 3x * (12 + 3x))
25 + 10x + 5x2 = ((144 + 36x) + 3x * (12 + 3x))
25 + 10x + 5x2 = (144 + 36x + (12 * 3x + 3x * 3x))
25 + 10x + 5x2 = (144 + 36x + (36x + 9x2))

Combine like terms: 36x + 36x = 72x
25 + 10x + 5x2 = (144 + 72x + 9x2)

Solving
25 + 10x + 5x2 = 144 + 72x + 9x2

Solving for variable 'x'.

Reorder the terms:
25 + -144 + 10x + -72x + 5x2 + -9x2 = 144 + 72x + 9x2 + -144 + -72x + -9x2

Combine like terms: 25 + -144 = -119
-119 + 10x + -72x + 5x2 + -9x2 = 144 + 72x + 9x2 + -144 + -72x + -9x2

Combine like terms: 10x + -72x = -62x
-119 + -62x + 5x2 + -9x2 = 144 + 72x + 9x2 + -144 + -72x + -9x2

Combine like terms: 5x2 + -9x2 = -4x2
-119 + -62x + -4x2 = 144 + 72x + 9x2 + -144 + -72x + -9x2

Reorder the terms:
-119 + -62x + -4x2 = 144 + -144 + 72x + -72x + 9x2 + -9x2

Combine like terms: 144 + -144 = 0
-119 + -62x + -4x2 = 0 + 72x + -72x + 9x2 + -9x2
-119 + -62x + -4x2 = 72x + -72x + 9x2 + -9x2

Combine like terms: 72x + -72x = 0
-119 + -62x + -4x2 = 0 + 9x2 + -9x2
-119 + -62x + -4x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
-119 + -62x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(119 + 62x + 4x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(119 + 62x + 4x2)' equal to zero and attempt to solve:

Simplifying
119 + 62x + 4x2 = 0

Solving
119 + 62x + 4x2 = 0

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

Divide each side by '4'.
29.75 + 15.5x + x2 = 0

Move the constant term to the right:

Add '-29.75' to each side of the equation.
29.75 + 15.5x + -29.75 + x2 = 0 + -29.75

Reorder the terms:
29.75 + -29.75 + 15.5x + x2 = 0 + -29.75

Combine like terms: 29.75 + -29.75 = 0.00
0.00 + 15.5x + x2 = 0 + -29.75
15.5x + x2 = 0 + -29.75

Combine like terms: 0 + -29.75 = -29.75
15.5x + x2 = -29.75

The x term is 15.5x.  Take half its coefficient (7.75).
Square it (60.0625) and add it to both sides.

Add '60.0625' to each side of the equation.
15.5x + 60.0625 + x2 = -29.75 + 60.0625

Reorder the terms:
60.0625 + 15.5x + x2 = -29.75 + 60.0625

Combine like terms: -29.75 + 60.0625 = 30.3125
60.0625 + 15.5x + x2 = 30.3125

Factor a perfect square on the left side:
(x + 7.75)(x + 7.75) = 30.3125

Calculate the square root of the right side: 5.505678886

Break this problem into two subproblems by setting 
(x + 7.75) equal to 5.505678886 and -5.505678886.


Subproblem 1
x + 7.75 = 5.505678886

Simplifying
x + 7.75 = 5.505678886

Reorder the terms:
7.75 + x = 5.505678886

Solving
7.75 + x = 5.505678886

Solving for variable 'x'.

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

Add '-7.75' to each side of the equation.
7.75 + -7.75 + x = 5.505678886 + -7.75

Combine like terms: 7.75 + -7.75 = 0.00
0.00 + x = 5.505678886 + -7.75
x = 5.505678886 + -7.75

Combine like terms: 5.505678886 + -7.75 = -2.244321114
x = -2.244321114

Simplifying
x = -2.244321114


Subproblem 2
x + 7.75 = -5.505678886

Simplifying
x + 7.75 = -5.505678886

Reorder the terms:
7.75 + x = -5.505678886

Solving
7.75 + x = -5.505678886

Solving for variable 'x'.

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

Add '-7.75' to each side of the equation.
7.75 + -7.75 + x = -5.505678886 + -7.75

Combine like terms: 7.75 + -7.75 = 0.00
0.00 + x = -5.505678886 + -7.75
x = -5.505678886 + -7.75

Combine like terms: -5.505678886 + -7.75 = -13.255678886
x = -13.255678886

Simplifying
x = -13.255678886


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.244321114, -13.255678886}
Solution
x = {-2.244321114, -13.255678886}

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