9x(3x-1)=2

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Solution for 9x(3x-1)=2 equation:


Simplifying
9x(3x + -1) = 2

Reorder the terms:
9x(-1 + 3x) = 2
(-1 * 9x + 3x * 9x) = 2
(-9x + 27x2) = 2

Solving
-9x + 27x2 = 2

Solving for variable 'x'.

Reorder the terms:
-2 + -9x + 27x2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + -9x + 27x2 = 0

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

Divide each side by '27'.
-0.07407407407 + -0.3333333333x + x2 = 0

Move the constant term to the right:

Add '0.07407407407' to each side of the equation.
-0.07407407407 + -0.3333333333x + 0.07407407407 + x2 = 0 + 0.07407407407

Reorder the terms:
-0.07407407407 + 0.07407407407 + -0.3333333333x + x2 = 0 + 0.07407407407

Combine like terms: -0.07407407407 + 0.07407407407 = 0.00000000000
0.00000000000 + -0.3333333333x + x2 = 0 + 0.07407407407
-0.3333333333x + x2 = 0 + 0.07407407407

Combine like terms: 0 + 0.07407407407 = 0.07407407407
-0.3333333333x + x2 = 0.07407407407

The x term is -0.3333333333x.  Take half its coefficient (-0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
-0.3333333333x + 0.02777777779 + x2 = 0.07407407407 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333x + x2 = 0.07407407407 + 0.02777777779

Combine like terms: 0.07407407407 + 0.02777777779 = 0.10185185186
0.02777777779 + -0.3333333333x + x2 = 0.10185185186

Factor a perfect square on the left side:
(x + -0.1666666667)(x + -0.1666666667) = 0.10185185186

Calculate the square root of the right side: 0.319142369

Break this problem into two subproblems by setting 
(x + -0.1666666667) equal to 0.319142369 and -0.319142369.

Subproblem 1

x + -0.1666666667 = 0.319142369 Simplifying x + -0.1666666667 = 0.319142369 Reorder the terms: -0.1666666667 + x = 0.319142369 Solving -0.1666666667 + x = 0.319142369 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = 0.319142369 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = 0.319142369 + 0.1666666667 x = 0.319142369 + 0.1666666667 Combine like terms: 0.319142369 + 0.1666666667 = 0.4858090357 x = 0.4858090357 Simplifying x = 0.4858090357

Subproblem 2

x + -0.1666666667 = -0.319142369 Simplifying x + -0.1666666667 = -0.319142369 Reorder the terms: -0.1666666667 + x = -0.319142369 Solving -0.1666666667 + x = -0.319142369 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = -0.319142369 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = -0.319142369 + 0.1666666667 x = -0.319142369 + 0.1666666667 Combine like terms: -0.319142369 + 0.1666666667 = -0.1524757023 x = -0.1524757023 Simplifying x = -0.1524757023

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.4858090357, -0.1524757023}

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