(x)(x)+(x+12)(x+12)=(x+6)(x+6)

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Solution for (x)(x)+(x+12)(x+12)=(x+6)(x+6) equation: 


Simplifying
(x)(x) + (x + 12)(x + 12) = (x + 6)(x + 6)

Multiply x * x
x2 + (x + 12)(x + 12) = (x + 6)(x + 6)

Reorder the terms:
x2 + (12 + x)(x + 12) = (x + 6)(x + 6)

Reorder the terms:
x2 + (12 + x)(12 + x) = (x + 6)(x + 6)

Multiply (12 + x) * (12 + x)
x2 + (12(12 + x) + x(12 + x)) = (x + 6)(x + 6)
x2 + ((12 * 12 + x * 12) + x(12 + x)) = (x + 6)(x + 6)
x2 + ((144 + 12x) + x(12 + x)) = (x + 6)(x + 6)
x2 + (144 + 12x + (12 * x + x * x)) = (x + 6)(x + 6)
x2 + (144 + 12x + (12x + x2)) = (x + 6)(x + 6)

Combine like terms: 12x + 12x = 24x
x2 + (144 + 24x + x2) = (x + 6)(x + 6)

Reorder the terms:
144 + 24x + x2 + x2 = (x + 6)(x + 6)

Combine like terms: x2 + x2 = 2x2
144 + 24x + 2x2 = (x + 6)(x + 6)

Reorder the terms:
144 + 24x + 2x2 = (6 + x)(x + 6)

Reorder the terms:
144 + 24x + 2x2 = (6 + x)(6 + x)

Multiply (6 + x) * (6 + x)
144 + 24x + 2x2 = (6(6 + x) + x(6 + x))
144 + 24x + 2x2 = ((6 * 6 + x * 6) + x(6 + x))
144 + 24x + 2x2 = ((36 + 6x) + x(6 + x))
144 + 24x + 2x2 = (36 + 6x + (6 * x + x * x))
144 + 24x + 2x2 = (36 + 6x + (6x + x2))

Combine like terms: 6x + 6x = 12x
144 + 24x + 2x2 = (36 + 12x + x2)

Solving
144 + 24x + 2x2 = 36 + 12x + x2

Solving for variable 'x'.

Reorder the terms:
144 + -36 + 24x + -12x + 2x2 + -1x2 = 36 + 12x + x2 + -36 + -12x + -1x2

Combine like terms: 144 + -36 = 108
108 + 24x + -12x + 2x2 + -1x2 = 36 + 12x + x2 + -36 + -12x + -1x2

Combine like terms: 24x + -12x = 12x
108 + 12x + 2x2 + -1x2 = 36 + 12x + x2 + -36 + -12x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
108 + 12x + 1x2 = 36 + 12x + x2 + -36 + -12x + -1x2

Reorder the terms:
108 + 12x + 1x2 = 36 + -36 + 12x + -12x + x2 + -1x2

Combine like terms: 36 + -36 = 0
108 + 12x + 1x2 = 0 + 12x + -12x + x2 + -1x2
108 + 12x + 1x2 = 12x + -12x + x2 + -1x2

Combine like terms: 12x + -12x = 0
108 + 12x + 1x2 = 0 + x2 + -1x2
108 + 12x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
108 + 12x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-108' to each side of the equation.
108 + 12x + -108 + x2 = 0 + -108

Reorder the terms:
108 + -108 + 12x + x2 = 0 + -108

Combine like terms: 108 + -108 = 0
0 + 12x + x2 = 0 + -108
12x + x2 = 0 + -108

Combine like terms: 0 + -108 = -108
12x + x2 = -108

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 = -108 + 36

Reorder the terms:
36 + 12x + x2 = -108 + 36

Combine like terms: -108 + 36 = -72
36 + 12x + x2 = -72

Factor a perfect square on the left side:
(x + 6)(x + 6) = -72

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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