9x^2-120x-2025=0

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Solution for 9x^2-120x-2025=0 equation:


Simplifying
9x2 + -120x + -2025 = 0

Reorder the terms:
-2025 + -120x + 9x2 = 0

Solving
-2025 + -120x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-675 + -40x + 3x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-675 + -40x + 3x2)' equal to zero and attempt to solve:

Simplifying
-675 + -40x + 3x2 = 0

Solving
-675 + -40x + 3x2 = 0

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

Divide each side by '3'.
-225 + -13.33333333x + x2 = 0

Move the constant term to the right:

Add '225' to each side of the equation.
-225 + -13.33333333x + 225 + x2 = 0 + 225

Reorder the terms:
-225 + 225 + -13.33333333x + x2 = 0 + 225

Combine like terms: -225 + 225 = 0
0 + -13.33333333x + x2 = 0 + 225
-13.33333333x + x2 = 0 + 225

Combine like terms: 0 + 225 = 225
-13.33333333x + x2 = 225

The x term is -13.33333333x.  Take half its coefficient (-6.666666665).
Square it (44.44444442) and add it to both sides.

Add '44.44444442' to each side of the equation.
-13.33333333x + 44.44444442 + x2 = 225 + 44.44444442

Reorder the terms:
44.44444442 + -13.33333333x + x2 = 225 + 44.44444442

Combine like terms: 225 + 44.44444442 = 269.44444442
44.44444442 + -13.33333333x + x2 = 269.44444442

Factor a perfect square on the left side:
(x + -6.666666665)(x + -6.666666665) = 269.44444442

Calculate the square root of the right side: 16.414763002

Break this problem into two subproblems by setting 
(x + -6.666666665) equal to 16.414763002 and -16.414763002.


Subproblem 1
x + -6.666666665 = 16.414763002

Simplifying
x + -6.666666665 = 16.414763002

Reorder the terms:
-6.666666665 + x = 16.414763002

Solving
-6.666666665 + x = 16.414763002

Solving for variable 'x'.

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

Add '6.666666665' to each side of the equation.
-6.666666665 + 6.666666665 + x = 16.414763002 + 6.666666665

Combine like terms: -6.666666665 + 6.666666665 = 0.000000000
0.000000000 + x = 16.414763002 + 6.666666665
x = 16.414763002 + 6.666666665

Combine like terms: 16.414763002 + 6.666666665 = 23.081429667
x = 23.081429667

Simplifying
x = 23.081429667


Subproblem 2
x + -6.666666665 = -16.414763002

Simplifying
x + -6.666666665 = -16.414763002

Reorder the terms:
-6.666666665 + x = -16.414763002

Solving
-6.666666665 + x = -16.414763002

Solving for variable 'x'.

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

Add '6.666666665' to each side of the equation.
-6.666666665 + 6.666666665 + x = -16.414763002 + 6.666666665

Combine like terms: -6.666666665 + 6.666666665 = 0.000000000
0.000000000 + x = -16.414763002 + 6.666666665
x = -16.414763002 + 6.666666665

Combine like terms: -16.414763002 + 6.666666665 = -9.748096337
x = -9.748096337

Simplifying
x = -9.748096337


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {23.081429667, -9.748096337}
Solution
x = {23.081429667, -9.748096337}

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