6(3x-1)(3x-1)+5=-17(3x+1)

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Solution for 6(3x-1)(3x-1)+5=-17(3x+1) equation:


Simplifying
6(3x + -1)(3x + -1) + 5 = -17(3x + 1)

Reorder the terms:
6(-1 + 3x)(3x + -1) + 5 = -17(3x + 1)

Reorder the terms:
6(-1 + 3x)(-1 + 3x) + 5 = -17(3x + 1)

Multiply (-1 + 3x) * (-1 + 3x)
6(-1(-1 + 3x) + 3x * (-1 + 3x)) + 5 = -17(3x + 1)
6((-1 * -1 + 3x * -1) + 3x * (-1 + 3x)) + 5 = -17(3x + 1)
6((1 + -3x) + 3x * (-1 + 3x)) + 5 = -17(3x + 1)
6(1 + -3x + (-1 * 3x + 3x * 3x)) + 5 = -17(3x + 1)
6(1 + -3x + (-3x + 9x2)) + 5 = -17(3x + 1)

Combine like terms: -3x + -3x = -6x
6(1 + -6x + 9x2) + 5 = -17(3x + 1)
(1 * 6 + -6x * 6 + 9x2 * 6) + 5 = -17(3x + 1)
(6 + -36x + 54x2) + 5 = -17(3x + 1)

Reorder the terms:
6 + 5 + -36x + 54x2 = -17(3x + 1)

Combine like terms: 6 + 5 = 11
11 + -36x + 54x2 = -17(3x + 1)

Reorder the terms:
11 + -36x + 54x2 = -17(1 + 3x)
11 + -36x + 54x2 = (1 * -17 + 3x * -17)
11 + -36x + 54x2 = (-17 + -51x)

Solving
11 + -36x + 54x2 = -17 + -51x

Solving for variable 'x'.

Reorder the terms:
11 + 17 + -36x + 51x + 54x2 = -17 + -51x + 17 + 51x

Combine like terms: 11 + 17 = 28
28 + -36x + 51x + 54x2 = -17 + -51x + 17 + 51x

Combine like terms: -36x + 51x = 15x
28 + 15x + 54x2 = -17 + -51x + 17 + 51x

Reorder the terms:
28 + 15x + 54x2 = -17 + 17 + -51x + 51x

Combine like terms: -17 + 17 = 0
28 + 15x + 54x2 = 0 + -51x + 51x
28 + 15x + 54x2 = -51x + 51x

Combine like terms: -51x + 51x = 0
28 + 15x + 54x2 = 0

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

Divide each side by '54'.
0.5185185185 + 0.2777777778x + x2 = 0

Move the constant term to the right:

Add '-0.5185185185' to each side of the equation.
0.5185185185 + 0.2777777778x + -0.5185185185 + x2 = 0 + -0.5185185185

Reorder the terms:
0.5185185185 + -0.5185185185 + 0.2777777778x + x2 = 0 + -0.5185185185

Combine like terms: 0.5185185185 + -0.5185185185 = 0.0000000000
0.0000000000 + 0.2777777778x + x2 = 0 + -0.5185185185
0.2777777778x + x2 = 0 + -0.5185185185

Combine like terms: 0 + -0.5185185185 = -0.5185185185
0.2777777778x + x2 = -0.5185185185

The x term is 0.2777777778x.  Take half its coefficient (0.1388888889).
Square it (0.01929012346) and add it to both sides.

Add '0.01929012346' to each side of the equation.
0.2777777778x + 0.01929012346 + x2 = -0.5185185185 + 0.01929012346

Reorder the terms:
0.01929012346 + 0.2777777778x + x2 = -0.5185185185 + 0.01929012346

Combine like terms: -0.5185185185 + 0.01929012346 = -0.49922839504
0.01929012346 + 0.2777777778x + x2 = -0.49922839504

Factor a perfect square on the left side:
(x + 0.1388888889)(x + 0.1388888889) = -0.49922839504

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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