(9(x)(x))-6x-38=0

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Solution for (9(x)(x))-6x-38=0 equation:


Simplifying
(9(x)(x)) + -6x + -38 = 0

Multiply x * x
(9x2) + -6x + -38 = 0

Reorder the terms:
-38 + -6x + (9x2) = 0

Solving
-38 + -6x + (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'.
-4.222222222 + -0.6666666667x + x2 = 0

Move the constant term to the right:

Add '4.222222222' to each side of the equation.
-4.222222222 + -0.6666666667x + 4.222222222 + x2 = 0 + 4.222222222

Reorder the terms:
-4.222222222 + 4.222222222 + -0.6666666667x + x2 = 0 + 4.222222222

Combine like terms: -4.222222222 + 4.222222222 = 0.000000000
0.000000000 + -0.6666666667x + x2 = 0 + 4.222222222
-0.6666666667x + x2 = 0 + 4.222222222

Combine like terms: 0 + 4.222222222 = 4.222222222
-0.6666666667x + x2 = 4.222222222

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 = 4.222222222 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667x + x2 = 4.222222222 + 0.1111111112

Combine like terms: 4.222222222 + 0.1111111112 = 4.3333333332
0.1111111112 + -0.6666666667x + x2 = 4.3333333332

Factor a perfect square on the left side:
((x) + -0.3333333334)((x) + -0.3333333334) = 4.3333333332

Calculate the square root of the right side: 2.081665999

Break this problem into two subproblems by setting 
((x) + -0.3333333334) equal to 2.081665999 and -2.081665999.

Subproblem 1

(x) + -0.3333333334 = 2.081665999 Simplifying (x) + -0.3333333334 = 2.081665999 x + -0.3333333334 = 2.081665999 Reorder the terms: -0.3333333334 + x = 2.081665999 Solving -0.3333333334 + x = 2.081665999 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 = 2.081665999 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = 2.081665999 + 0.3333333334 x = 2.081665999 + 0.3333333334 Combine like terms: 2.081665999 + 0.3333333334 = 2.4149993324 x = 2.4149993324 Simplifying x = 2.4149993324

Subproblem 2

(x) + -0.3333333334 = -2.081665999 Simplifying (x) + -0.3333333334 = -2.081665999 x + -0.3333333334 = -2.081665999 Reorder the terms: -0.3333333334 + x = -2.081665999 Solving -0.3333333334 + x = -2.081665999 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 = -2.081665999 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = -2.081665999 + 0.3333333334 x = -2.081665999 + 0.3333333334 Combine like terms: -2.081665999 + 0.3333333334 = -1.7483326656 x = -1.7483326656 Simplifying x = -1.7483326656

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.4149993324, -1.7483326656}

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