828x=9(x^2-19x+12960)

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Solution for 828x=9(x^2-19x+12960) equation: 


Simplifying
828x = 9(x2 + -19x + 12960)

Reorder the terms:
828x = 9(12960 + -19x + x2)
828x = (12960 * 9 + -19x * 9 + x2 * 9)
828x = (116640 + -171x + 9x2)

Solving
828x = 116640 + -171x + 9x2

Solving for variable 'x'.

Reorder the terms:
-116640 + 828x + 171x + -9x2 = 116640 + -171x + 9x2 + -116640 + 171x + -9x2

Combine like terms: 828x + 171x = 999x
-116640 + 999x + -9x2 = 116640 + -171x + 9x2 + -116640 + 171x + -9x2

Reorder the terms:
-116640 + 999x + -9x2 = 116640 + -116640 + -171x + 171x + 9x2 + -9x2

Combine like terms: 116640 + -116640 = 0
-116640 + 999x + -9x2 = 0 + -171x + 171x + 9x2 + -9x2
-116640 + 999x + -9x2 = -171x + 171x + 9x2 + -9x2

Combine like terms: -171x + 171x = 0
-116640 + 999x + -9x2 = 0 + 9x2 + -9x2
-116640 + 999x + -9x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
-116640 + 999x + -9x2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(-12960 + 111x + -1x2) = 0

Ignore the factor 9.

Subproblem 1
Set the factor '(-12960 + 111x + -1x2)' equal to zero and attempt to solve:

Simplifying
-12960 + 111x + -1x2 = 0

Solving
-12960 + 111x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
12960 + -111x + x2 = 0

Move the constant term to the right:

Add '-12960' to each side of the equation.
12960 + -111x + -12960 + x2 = 0 + -12960

Reorder the terms:
12960 + -12960 + -111x + x2 = 0 + -12960

Combine like terms: 12960 + -12960 = 0
0 + -111x + x2 = 0 + -12960
-111x + x2 = 0 + -12960

Combine like terms: 0 + -12960 = -12960
-111x + x2 = -12960

The x term is -111x.  Take half its coefficient (-55.5).
Square it (3080.25) and add it to both sides.

Add '3080.25' to each side of the equation.
-111x + 3080.25 + x2 = -12960 + 3080.25

Reorder the terms:
3080.25 + -111x + x2 = -12960 + 3080.25

Combine like terms: -12960 + 3080.25 = -9879.75
3080.25 + -111x + x2 = -9879.75

Factor a perfect square on the left side:
(x + -55.5)(x + -55.5) = -9879.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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