9x^2-42x-64=0

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Solution for 9x^2-42x-64=0 equation: 


Simplifying
9x2 + -42x + -64 = 0

Reorder the terms:
-64 + -42x + 9x2 = 0

Solving
-64 + -42x + 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'.
-7.111111111 + -4.666666667x + x2 = 0

Move the constant term to the right:

Add '7.111111111' to each side of the equation.
-7.111111111 + -4.666666667x + 7.111111111 + x2 = 0 + 7.111111111

Reorder the terms:
-7.111111111 + 7.111111111 + -4.666666667x + x2 = 0 + 7.111111111

Combine like terms: -7.111111111 + 7.111111111 = 0.000000000
0.000000000 + -4.666666667x + x2 = 0 + 7.111111111
-4.666666667x + x2 = 0 + 7.111111111

Combine like terms: 0 + 7.111111111 = 7.111111111
-4.666666667x + x2 = 7.111111111

The x term is -4.666666667x.  Take half its coefficient (-2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
-4.666666667x + 5.444444448 + x2 = 7.111111111 + 5.444444448

Reorder the terms:
5.444444448 + -4.666666667x + x2 = 7.111111111 + 5.444444448

Combine like terms: 7.111111111 + 5.444444448 = 12.555555559
5.444444448 + -4.666666667x + x2 = 12.555555559

Factor a perfect square on the left side:
(x + -2.333333334)(x + -2.333333334) = 12.555555559

Calculate the square root of the right side: 3.543381938

Break this problem into two subproblems by setting 
(x + -2.333333334) equal to 3.543381938 and -3.543381938.


Subproblem 1
x + -2.333333334 = 3.543381938

Simplifying
x + -2.333333334 = 3.543381938

Reorder the terms:
-2.333333334 + x = 3.543381938

Solving
-2.333333334 + x = 3.543381938

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + x = 3.543381938 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = 3.543381938 + 2.333333334
x = 3.543381938 + 2.333333334

Combine like terms: 3.543381938 + 2.333333334 = 5.876715272
x = 5.876715272

Simplifying
x = 5.876715272


Subproblem 2
x + -2.333333334 = -3.543381938

Simplifying
x + -2.333333334 = -3.543381938

Reorder the terms:
-2.333333334 + x = -3.543381938

Solving
-2.333333334 + x = -3.543381938

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + x = -3.543381938 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = -3.543381938 + 2.333333334
x = -3.543381938 + 2.333333334

Combine like terms: -3.543381938 + 2.333333334 = -1.210048604
x = -1.210048604

Simplifying
x = -1.210048604


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.876715272, -1.210048604}

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