9x^2-64x-3600=0

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Solution for 9x^2-64x-3600=0 equation: 


Simplifying
9x2 + -64x + -3600 = 0

Reorder the terms:
-3600 + -64x + 9x2 = 0

Solving
-3600 + -64x + 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'.
-400 + -7.111111111x + x2 = 0

Move the constant term to the right:

Add '400' to each side of the equation.
-400 + -7.111111111x + 400 + x2 = 0 + 400

Reorder the terms:
-400 + 400 + -7.111111111x + x2 = 0 + 400

Combine like terms: -400 + 400 = 0
0 + -7.111111111x + x2 = 0 + 400
-7.111111111x + x2 = 0 + 400

Combine like terms: 0 + 400 = 400
-7.111111111x + x2 = 400

The x term is -7.111111111x.  Take half its coefficient (-3.555555556).
Square it (12.64197531) and add it to both sides.

Add '12.64197531' to each side of the equation.
-7.111111111x + 12.64197531 + x2 = 400 + 12.64197531

Reorder the terms:
12.64197531 + -7.111111111x + x2 = 400 + 12.64197531

Combine like terms: 400 + 12.64197531 = 412.64197531
12.64197531 + -7.111111111x + x2 = 412.64197531

Factor a perfect square on the left side:
(x + -3.555555556)(x + -3.555555556) = 412.64197531

Calculate the square root of the right side: 20.313590901

Break this problem into two subproblems by setting 
(x + -3.555555556) equal to 20.313590901 and -20.313590901.


Subproblem 1
x + -3.555555556 = 20.313590901

Simplifying
x + -3.555555556 = 20.313590901

Reorder the terms:
-3.555555556 + x = 20.313590901

Solving
-3.555555556 + x = 20.313590901

Solving for variable 'x'.

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

Add '3.555555556' to each side of the equation.
-3.555555556 + 3.555555556 + x = 20.313590901 + 3.555555556

Combine like terms: -3.555555556 + 3.555555556 = 0.000000000
0.000000000 + x = 20.313590901 + 3.555555556
x = 20.313590901 + 3.555555556

Combine like terms: 20.313590901 + 3.555555556 = 23.869146457
x = 23.869146457

Simplifying
x = 23.869146457


Subproblem 2
x + -3.555555556 = -20.313590901

Simplifying
x + -3.555555556 = -20.313590901

Reorder the terms:
-3.555555556 + x = -20.313590901

Solving
-3.555555556 + x = -20.313590901

Solving for variable 'x'.

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

Add '3.555555556' to each side of the equation.
-3.555555556 + 3.555555556 + x = -20.313590901 + 3.555555556

Combine like terms: -3.555555556 + 3.555555556 = 0.000000000
0.000000000 + x = -20.313590901 + 3.555555556
x = -20.313590901 + 3.555555556

Combine like terms: -20.313590901 + 3.555555556 = -16.758035345
x = -16.758035345

Simplifying
x = -16.758035345


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {23.869146457, -16.758035345}

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