9x^2-12x=13

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Solution for 9x^2-12x=13 equation:


Simplifying
9x2 + -12x = 13

Reorder the terms:
-12x + 9x2 = 13

Solving
-12x + 9x2 = 13

Solving for variable 'x'.

Reorder the terms:
-13 + -12x + 9x2 = 13 + -13

Combine like terms: 13 + -13 = 0
-13 + -12x + 9x2 = 0

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

Divide each side by '9'.
-1.444444444 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '1.444444444' to each side of the equation.
-1.444444444 + -1.333333333x + 1.444444444 + x2 = 0 + 1.444444444

Reorder the terms:
-1.444444444 + 1.444444444 + -1.333333333x + x2 = 0 + 1.444444444

Combine like terms: -1.444444444 + 1.444444444 = 0.000000000
0.000000000 + -1.333333333x + x2 = 0 + 1.444444444
-1.333333333x + x2 = 0 + 1.444444444

Combine like terms: 0 + 1.444444444 = 1.444444444
-1.333333333x + x2 = 1.444444444

The x term is -1.333333333x.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333x + 0.4444444442 + x2 = 1.444444444 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = 1.444444444 + 0.4444444442

Combine like terms: 1.444444444 + 0.4444444442 = 1.8888888882
0.4444444442 + -1.333333333x + x2 = 1.8888888882

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = 1.8888888882

Calculate the square root of the right side: 1.374368542

Break this problem into two subproblems by setting 
(x + -0.6666666665) equal to 1.374368542 and -1.374368542.

Subproblem 1

x + -0.6666666665 = 1.374368542 Simplifying x + -0.6666666665 = 1.374368542 Reorder the terms: -0.6666666665 + x = 1.374368542 Solving -0.6666666665 + x = 1.374368542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = 1.374368542 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 1.374368542 + 0.6666666665 x = 1.374368542 + 0.6666666665 Combine like terms: 1.374368542 + 0.6666666665 = 2.0410352085 x = 2.0410352085 Simplifying x = 2.0410352085

Subproblem 2

x + -0.6666666665 = -1.374368542 Simplifying x + -0.6666666665 = -1.374368542 Reorder the terms: -0.6666666665 + x = -1.374368542 Solving -0.6666666665 + x = -1.374368542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = -1.374368542 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -1.374368542 + 0.6666666665 x = -1.374368542 + 0.6666666665 Combine like terms: -1.374368542 + 0.6666666665 = -0.7077018755 x = -0.7077018755 Simplifying x = -0.7077018755

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.0410352085, -0.7077018755}

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