9x^2-14x-12=0

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Solution for 9x^2-14x-12=0 equation:


Simplifying
9x2 + -14x + -12 = 0

Reorder the terms:
-12 + -14x + 9x2 = 0

Solving
-12 + -14x + 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 + -1.555555556x + x2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + -1.555555556x + 1.333333333 + x2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + -1.555555556x + x2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + -1.555555556x + x2 = 0 + 1.333333333
-1.555555556x + x2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
-1.555555556x + x2 = 1.333333333

The x term is -1.555555556x.  Take half its coefficient (-0.777777778).
Square it (0.6049382720) and add it to both sides.

Add '0.6049382720' to each side of the equation.
-1.555555556x + 0.6049382720 + x2 = 1.333333333 + 0.6049382720

Reorder the terms:
0.6049382720 + -1.555555556x + x2 = 1.333333333 + 0.6049382720

Combine like terms: 1.333333333 + 0.6049382720 = 1.938271605
0.6049382720 + -1.555555556x + x2 = 1.938271605

Factor a perfect square on the left side:
(x + -0.777777778)(x + -0.777777778) = 1.938271605

Calculate the square root of the right side: 1.392218232

Break this problem into two subproblems by setting 
(x + -0.777777778) equal to 1.392218232 and -1.392218232.

Subproblem 1

x + -0.777777778 = 1.392218232 Simplifying x + -0.777777778 = 1.392218232 Reorder the terms: -0.777777778 + x = 1.392218232 Solving -0.777777778 + x = 1.392218232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.777777778' to each side of the equation. -0.777777778 + 0.777777778 + x = 1.392218232 + 0.777777778 Combine like terms: -0.777777778 + 0.777777778 = 0.000000000 0.000000000 + x = 1.392218232 + 0.777777778 x = 1.392218232 + 0.777777778 Combine like terms: 1.392218232 + 0.777777778 = 2.16999601 x = 2.16999601 Simplifying x = 2.16999601

Subproblem 2

x + -0.777777778 = -1.392218232 Simplifying x + -0.777777778 = -1.392218232 Reorder the terms: -0.777777778 + x = -1.392218232 Solving -0.777777778 + x = -1.392218232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.777777778' to each side of the equation. -0.777777778 + 0.777777778 + x = -1.392218232 + 0.777777778 Combine like terms: -0.777777778 + 0.777777778 = 0.000000000 0.000000000 + x = -1.392218232 + 0.777777778 x = -1.392218232 + 0.777777778 Combine like terms: -1.392218232 + 0.777777778 = -0.614440454 x = -0.614440454 Simplifying x = -0.614440454

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.16999601, -0.614440454}

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