9x^2+6x-x-22x+12=12x

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Solution for 9x^2+6x-x-22x+12=12x equation:


Simplifying
9x2 + 6x + -1x + -22x + 12 = 12x

Reorder the terms:
12 + 6x + -1x + -22x + 9x2 = 12x

Combine like terms: 6x + -1x = 5x
12 + 5x + -22x + 9x2 = 12x

Combine like terms: 5x + -22x = -17x
12 + -17x + 9x2 = 12x

Solving
12 + -17x + 9x2 = 12x

Solving for variable 'x'.

Reorder the terms:
12 + -17x + -12x + 9x2 = 12x + -12x

Combine like terms: -17x + -12x = -29x
12 + -29x + 9x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
12 + -29x + 9x2 = 0

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

Divide each side by '9'.
1.333333333 + -3.222222222x + x2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + -3.222222222x + -1.333333333 + x2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + -3.222222222x + x2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + -3.222222222x + x2 = 0 + -1.333333333
-3.222222222x + x2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
-3.222222222x + x2 = -1.333333333

The x term is -3.222222222x.  Take half its coefficient (-1.611111111).
Square it (2.595679012) and add it to both sides.

Add '2.595679012' to each side of the equation.
-3.222222222x + 2.595679012 + x2 = -1.333333333 + 2.595679012

Reorder the terms:
2.595679012 + -3.222222222x + x2 = -1.333333333 + 2.595679012

Combine like terms: -1.333333333 + 2.595679012 = 1.262345679
2.595679012 + -3.222222222x + x2 = 1.262345679

Factor a perfect square on the left side:
(x + -1.611111111)(x + -1.611111111) = 1.262345679

Calculate the square root of the right side: 1.123541579

Break this problem into two subproblems by setting 
(x + -1.611111111) equal to 1.123541579 and -1.123541579.

Subproblem 1

x + -1.611111111 = 1.123541579 Simplifying x + -1.611111111 = 1.123541579 Reorder the terms: -1.611111111 + x = 1.123541579 Solving -1.611111111 + x = 1.123541579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.611111111' to each side of the equation. -1.611111111 + 1.611111111 + x = 1.123541579 + 1.611111111 Combine like terms: -1.611111111 + 1.611111111 = 0.000000000 0.000000000 + x = 1.123541579 + 1.611111111 x = 1.123541579 + 1.611111111 Combine like terms: 1.123541579 + 1.611111111 = 2.73465269 x = 2.73465269 Simplifying x = 2.73465269

Subproblem 2

x + -1.611111111 = -1.123541579 Simplifying x + -1.611111111 = -1.123541579 Reorder the terms: -1.611111111 + x = -1.123541579 Solving -1.611111111 + x = -1.123541579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.611111111' to each side of the equation. -1.611111111 + 1.611111111 + x = -1.123541579 + 1.611111111 Combine like terms: -1.611111111 + 1.611111111 = 0.000000000 0.000000000 + x = -1.123541579 + 1.611111111 x = -1.123541579 + 1.611111111 Combine like terms: -1.123541579 + 1.611111111 = 0.487569532 x = 0.487569532 Simplifying x = 0.487569532

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.73465269, 0.487569532}

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