(3x-3)(3x+2)=29

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Solution for (3x-3)(3x+2)=29 equation:


Simplifying
(3x + -3)(3x + 2) = 29

Reorder the terms:
(-3 + 3x)(3x + 2) = 29

Reorder the terms:
(-3 + 3x)(2 + 3x) = 29

Multiply (-3 + 3x) * (2 + 3x)
(-3(2 + 3x) + 3x * (2 + 3x)) = 29
((2 * -3 + 3x * -3) + 3x * (2 + 3x)) = 29
((-6 + -9x) + 3x * (2 + 3x)) = 29
(-6 + -9x + (2 * 3x + 3x * 3x)) = 29
(-6 + -9x + (6x + 9x2)) = 29

Combine like terms: -9x + 6x = -3x
(-6 + -3x + 9x2) = 29

Solving
-6 + -3x + 9x2 = 29

Solving for variable 'x'.

Reorder the terms:
-6 + -29 + -3x + 9x2 = 29 + -29

Combine like terms: -6 + -29 = -35
-35 + -3x + 9x2 = 29 + -29

Combine like terms: 29 + -29 = 0
-35 + -3x + 9x2 = 0

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

Divide each side by '9'.
-3.888888889 + -0.3333333333x + x2 = 0

Move the constant term to the right:

Add '3.888888889' to each side of the equation.
-3.888888889 + -0.3333333333x + 3.888888889 + x2 = 0 + 3.888888889

Reorder the terms:
-3.888888889 + 3.888888889 + -0.3333333333x + x2 = 0 + 3.888888889

Combine like terms: -3.888888889 + 3.888888889 = 0.000000000
0.000000000 + -0.3333333333x + x2 = 0 + 3.888888889
-0.3333333333x + x2 = 0 + 3.888888889

Combine like terms: 0 + 3.888888889 = 3.888888889
-0.3333333333x + x2 = 3.888888889

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 = 3.888888889 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333x + x2 = 3.888888889 + 0.02777777779

Combine like terms: 3.888888889 + 0.02777777779 = 3.91666666679
0.02777777779 + -0.3333333333x + x2 = 3.91666666679

Factor a perfect square on the left side:
(x + -0.1666666667)(x + -0.1666666667) = 3.91666666679

Calculate the square root of the right side: 1.979057015

Break this problem into two subproblems by setting 
(x + -0.1666666667) equal to 1.979057015 and -1.979057015.

Subproblem 1

x + -0.1666666667 = 1.979057015 Simplifying x + -0.1666666667 = 1.979057015 Reorder the terms: -0.1666666667 + x = 1.979057015 Solving -0.1666666667 + x = 1.979057015 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 = 1.979057015 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = 1.979057015 + 0.1666666667 x = 1.979057015 + 0.1666666667 Combine like terms: 1.979057015 + 0.1666666667 = 2.1457236817 x = 2.1457236817 Simplifying x = 2.1457236817

Subproblem 2

x + -0.1666666667 = -1.979057015 Simplifying x + -0.1666666667 = -1.979057015 Reorder the terms: -0.1666666667 + x = -1.979057015 Solving -0.1666666667 + x = -1.979057015 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 = -1.979057015 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = -1.979057015 + 0.1666666667 x = -1.979057015 + 0.1666666667 Combine like terms: -1.979057015 + 0.1666666667 = -1.8123903483 x = -1.8123903483 Simplifying x = -1.8123903483

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.1457236817, -1.8123903483}

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