9x^2-30x-64=0

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Solution for 9x^2-30x-64=0 equation: 


Simplifying
9x2 + -30x + -64 = 0

Reorder the terms:
-64 + -30x + 9x2 = 0

Solving
-64 + -30x + 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 + -3.333333333x + x2 = 0

Move the constant term to the right:

Add '7.111111111' to each side of the equation.
-7.111111111 + -3.333333333x + 7.111111111 + x2 = 0 + 7.111111111

Reorder the terms:
-7.111111111 + 7.111111111 + -3.333333333x + x2 = 0 + 7.111111111

Combine like terms: -7.111111111 + 7.111111111 = 0.000000000
0.000000000 + -3.333333333x + x2 = 0 + 7.111111111
-3.333333333x + x2 = 0 + 7.111111111

Combine like terms: 0 + 7.111111111 = 7.111111111
-3.333333333x + x2 = 7.111111111

The x term is -3.333333333x.  Take half its coefficient (-1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
-3.333333333x + 2.777777779 + x2 = 7.111111111 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333x + x2 = 7.111111111 + 2.777777779

Combine like terms: 7.111111111 + 2.777777779 = 9.88888889
2.777777779 + -3.333333333x + x2 = 9.88888889

Factor a perfect square on the left side:
(x + -1.666666667)(x + -1.666666667) = 9.88888889

Calculate the square root of the right side: 3.144660378

Break this problem into two subproblems by setting 
(x + -1.666666667) equal to 3.144660378 and -3.144660378.


Subproblem 1
x + -1.666666667 = 3.144660378

Simplifying
x + -1.666666667 = 3.144660378

Reorder the terms:
-1.666666667 + x = 3.144660378

Solving
-1.666666667 + x = 3.144660378

Solving for variable 'x'.

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

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + x = 3.144660378 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + x = 3.144660378 + 1.666666667
x = 3.144660378 + 1.666666667

Combine like terms: 3.144660378 + 1.666666667 = 4.811327045
x = 4.811327045

Simplifying
x = 4.811327045


Subproblem 2
x + -1.666666667 = -3.144660378

Simplifying
x + -1.666666667 = -3.144660378

Reorder the terms:
-1.666666667 + x = -3.144660378

Solving
-1.666666667 + x = -3.144660378

Solving for variable 'x'.

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

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + x = -3.144660378 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + x = -3.144660378 + 1.666666667
x = -3.144660378 + 1.666666667

Combine like terms: -3.144660378 + 1.666666667 = -1.477993711
x = -1.477993711

Simplifying
x = -1.477993711


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.811327045, -1.477993711}

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