9x^2-6x=16

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Solution for 9x^2-6x=16 equation:


Simplifying
9x2 + -6x = 16

Reorder the terms:
-6x + 9x2 = 16

Solving
-6x + 9x2 = 16

Solving for variable 'x'.

Reorder the terms:
-16 + -6x + 9x2 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + -6x + 9x2 = 0

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

Divide each side by '9'.
-1.777777778 + -0.6666666667x + x2 = 0

Move the constant term to the right:

Add '1.777777778' to each side of the equation.
-1.777777778 + -0.6666666667x + 1.777777778 + x2 = 0 + 1.777777778

Reorder the terms:
-1.777777778 + 1.777777778 + -0.6666666667x + x2 = 0 + 1.777777778

Combine like terms: -1.777777778 + 1.777777778 = 0.000000000
0.000000000 + -0.6666666667x + x2 = 0 + 1.777777778
-0.6666666667x + x2 = 0 + 1.777777778

Combine like terms: 0 + 1.777777778 = 1.777777778
-0.6666666667x + x2 = 1.777777778

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 = 1.777777778 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667x + x2 = 1.777777778 + 0.1111111112

Combine like terms: 1.777777778 + 0.1111111112 = 1.8888888892
0.1111111112 + -0.6666666667x + x2 = 1.8888888892

Factor a perfect square on the left side:
(x + -0.3333333334)(x + -0.3333333334) = 1.8888888892

Calculate the square root of the right side: 1.374368542

Break this problem into two subproblems by setting 
(x + -0.3333333334) equal to 1.374368542 and -1.374368542.

Subproblem 1

x + -0.3333333334 = 1.374368542 Simplifying x + -0.3333333334 = 1.374368542 Reorder the terms: -0.3333333334 + x = 1.374368542 Solving -0.3333333334 + x = 1.374368542 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 = 1.374368542 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = 1.374368542 + 0.3333333334 x = 1.374368542 + 0.3333333334 Combine like terms: 1.374368542 + 0.3333333334 = 1.7077018754 x = 1.7077018754 Simplifying x = 1.7077018754

Subproblem 2

x + -0.3333333334 = -1.374368542 Simplifying x + -0.3333333334 = -1.374368542 Reorder the terms: -0.3333333334 + x = -1.374368542 Solving -0.3333333334 + x = -1.374368542 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 = -1.374368542 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = -1.374368542 + 0.3333333334 x = -1.374368542 + 0.3333333334 Combine like terms: -1.374368542 + 0.3333333334 = -1.0410352086 x = -1.0410352086 Simplifying x = -1.0410352086

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.7077018754, -1.0410352086}

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