(3x)(3x)-x-12=0

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Solution for (3x)(3x)-x-12=0 equation:


Simplifying
(3x)(3x) + -1x + -12 = 0

Remove parenthesis around (3x)
3x(3x) + -1x + -12 = 0

Remove parenthesis around (3x)
3x * 3x + -1x + -12 = 0

Reorder the terms for easier multiplication:
3 * 3x * x + -1x + -12 = 0

Multiply 3 * 3
9x * x + -1x + -12 = 0

Multiply x * x
9x2 + -1x + -12 = 0

Reorder the terms:
-12 + -1x + 9x2 = 0

Solving
-12 + -1x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
-1.333333333 + -0.1111111111x + x2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + -0.1111111111x + 1.333333333 + x2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + -0.1111111111x + x2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + -0.1111111111x + x2 = 0 + 1.333333333
-0.1111111111x + x2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
-0.1111111111x + x2 = 1.333333333

The x term is -0.1111111111x.  Take half its coefficient (-0.05555555555).
Square it (0.003086419752) and add it to both sides.

Add '0.003086419752' to each side of the equation.
-0.1111111111x + 0.003086419752 + x2 = 1.333333333 + 0.003086419752

Reorder the terms:
0.003086419752 + -0.1111111111x + x2 = 1.333333333 + 0.003086419752

Combine like terms: 1.333333333 + 0.003086419752 = 1.336419752752
0.003086419752 + -0.1111111111x + x2 = 1.336419752752

Factor a perfect square on the left side:
(x + -0.05555555555)(x + -0.05555555555) = 1.336419752752

Calculate the square root of the right side: 1.156036225

Break this problem into two subproblems by setting 
(x + -0.05555555555) equal to 1.156036225 and -1.156036225.

Subproblem 1

x + -0.05555555555 = 1.156036225 Simplifying x + -0.05555555555 = 1.156036225 Reorder the terms: -0.05555555555 + x = 1.156036225 Solving -0.05555555555 + x = 1.156036225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05555555555' to each side of the equation. -0.05555555555 + 0.05555555555 + x = 1.156036225 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + x = 1.156036225 + 0.05555555555 x = 1.156036225 + 0.05555555555 Combine like terms: 1.156036225 + 0.05555555555 = 1.21159178055 x = 1.21159178055 Simplifying x = 1.21159178055

Subproblem 2

x + -0.05555555555 = -1.156036225 Simplifying x + -0.05555555555 = -1.156036225 Reorder the terms: -0.05555555555 + x = -1.156036225 Solving -0.05555555555 + x = -1.156036225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05555555555' to each side of the equation. -0.05555555555 + 0.05555555555 + x = -1.156036225 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + x = -1.156036225 + 0.05555555555 x = -1.156036225 + 0.05555555555 Combine like terms: -1.156036225 + 0.05555555555 = -1.10048066945 x = -1.10048066945 Simplifying x = -1.10048066945

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.21159178055, -1.10048066945}

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