9x^2-6x-14=-12x

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Solution for 9x^2-6x-14=-12x equation:


Simplifying
9x2 + -6x + -14 = -12x

Reorder the terms:
-14 + -6x + 9x2 = -12x

Solving
-14 + -6x + 9x2 = -12x

Solving for variable 'x'.

Reorder the terms:
-14 + -6x + 12x + 9x2 = -12x + 12x

Combine like terms: -6x + 12x = 6x
-14 + 6x + 9x2 = -12x + 12x

Combine like terms: -12x + 12x = 0
-14 + 6x + 9x2 = 0

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

Divide each side by '9'.
-1.555555556 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '1.555555556' to each side of the equation.
-1.555555556 + 0.6666666667x + 1.555555556 + x2 = 0 + 1.555555556

Reorder the terms:
-1.555555556 + 1.555555556 + 0.6666666667x + x2 = 0 + 1.555555556

Combine like terms: -1.555555556 + 1.555555556 = 0.000000000
0.000000000 + 0.6666666667x + x2 = 0 + 1.555555556
0.6666666667x + x2 = 0 + 1.555555556

Combine like terms: 0 + 1.555555556 = 1.555555556
0.6666666667x + x2 = 1.555555556

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = 1.555555556 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 1.555555556 + 0.1111111112

Combine like terms: 1.555555556 + 0.1111111112 = 1.6666666672
0.1111111112 + 0.6666666667x + x2 = 1.6666666672

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 1.6666666672

Calculate the square root of the right side: 1.290994449

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 1.290994449 and -1.290994449.

Subproblem 1

x + 0.3333333334 = 1.290994449 Simplifying x + 0.3333333334 = 1.290994449 Reorder the terms: 0.3333333334 + x = 1.290994449 Solving 0.3333333334 + x = 1.290994449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 1.290994449 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 1.290994449 + -0.3333333334 x = 1.290994449 + -0.3333333334 Combine like terms: 1.290994449 + -0.3333333334 = 0.9576611156 x = 0.9576611156 Simplifying x = 0.9576611156

Subproblem 2

x + 0.3333333334 = -1.290994449 Simplifying x + 0.3333333334 = -1.290994449 Reorder the terms: 0.3333333334 + x = -1.290994449 Solving 0.3333333334 + x = -1.290994449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -1.290994449 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -1.290994449 + -0.3333333334 x = -1.290994449 + -0.3333333334 Combine like terms: -1.290994449 + -0.3333333334 = -1.6243277824 x = -1.6243277824 Simplifying x = -1.6243277824

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.9576611156, -1.6243277824}

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