3x(3x+1)=5(x-7)

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Solution for 3x(3x+1)=5(x-7) equation:


Simplifying
3x(3x + 1) = 5(x + -7)

Reorder the terms:
3x(1 + 3x) = 5(x + -7)
(1 * 3x + 3x * 3x) = 5(x + -7)
(3x + 9x2) = 5(x + -7)

Reorder the terms:
3x + 9x2 = 5(-7 + x)
3x + 9x2 = (-7 * 5 + x * 5)
3x + 9x2 = (-35 + 5x)

Solving
3x + 9x2 = -35 + 5x

Solving for variable 'x'.

Reorder the terms:
35 + 3x + -5x + 9x2 = -35 + 5x + 35 + -5x

Combine like terms: 3x + -5x = -2x
35 + -2x + 9x2 = -35 + 5x + 35 + -5x

Reorder the terms:
35 + -2x + 9x2 = -35 + 35 + 5x + -5x

Combine like terms: -35 + 35 = 0
35 + -2x + 9x2 = 0 + 5x + -5x
35 + -2x + 9x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
35 + -2x + 9x2 = 0

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

Divide each side by '9'.
3.888888889 + -0.2222222222x + x2 = 0

Move the constant term to the right:

Add '-3.888888889' to each side of the equation.
3.888888889 + -0.2222222222x + -3.888888889 + x2 = 0 + -3.888888889

Reorder the terms:
3.888888889 + -3.888888889 + -0.2222222222x + x2 = 0 + -3.888888889

Combine like terms: 3.888888889 + -3.888888889 = 0.000000000
0.000000000 + -0.2222222222x + x2 = 0 + -3.888888889
-0.2222222222x + x2 = 0 + -3.888888889

Combine like terms: 0 + -3.888888889 = -3.888888889
-0.2222222222x + x2 = -3.888888889

The x term is -0.2222222222x.  Take half its coefficient (-0.1111111111).
Square it (0.01234567901) and add it to both sides.

Add '0.01234567901' to each side of the equation.
-0.2222222222x + 0.01234567901 + x2 = -3.888888889 + 0.01234567901

Reorder the terms:
0.01234567901 + -0.2222222222x + x2 = -3.888888889 + 0.01234567901

Combine like terms: -3.888888889 + 0.01234567901 = -3.87654320999
0.01234567901 + -0.2222222222x + x2 = -3.87654320999

Factor a perfect square on the left side:
(x + -0.1111111111)(x + -0.1111111111) = -3.87654320999

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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