480x-2x^2-480=0

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Solution for 480x-2x^2-480=0 equation: 


Simplifying
480x + -2x2 + -480 = 0

Reorder the terms:
-480 + 480x + -2x2 = 0

Solving
-480 + 480x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-240 + 240x + -1x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-240 + 240x + -1x2)' equal to zero and attempt to solve:

Simplifying
-240 + 240x + -1x2 = 0

Solving
-240 + 240x + -1x2 = 0

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

Divide each side by '-1'.
240 + -240x + x2 = 0

Move the constant term to the right:

Add '-240' to each side of the equation.
240 + -240x + -240 + x2 = 0 + -240

Reorder the terms:
240 + -240 + -240x + x2 = 0 + -240

Combine like terms: 240 + -240 = 0
0 + -240x + x2 = 0 + -240
-240x + x2 = 0 + -240

Combine like terms: 0 + -240 = -240
-240x + x2 = -240

The x term is -240x.  Take half its coefficient (-120).
Square it (14400) and add it to both sides.

Add '14400' to each side of the equation.
-240x + 14400 + x2 = -240 + 14400

Reorder the terms:
14400 + -240x + x2 = -240 + 14400

Combine like terms: -240 + 14400 = 14160
14400 + -240x + x2 = 14160

Factor a perfect square on the left side:
(x + -120)(x + -120) = 14160

Calculate the square root of the right side: 118.995798245

Break this problem into two subproblems by setting 
(x + -120) equal to 118.995798245 and -118.995798245.


Subproblem 1
x + -120 = 118.995798245

Simplifying
x + -120 = 118.995798245

Reorder the terms:
-120 + x = 118.995798245

Solving
-120 + x = 118.995798245

Solving for variable 'x'.

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

Add '120' to each side of the equation.
-120 + 120 + x = 118.995798245 + 120

Combine like terms: -120 + 120 = 0
0 + x = 118.995798245 + 120
x = 118.995798245 + 120

Combine like terms: 118.995798245 + 120 = 238.995798245
x = 238.995798245

Simplifying
x = 238.995798245


Subproblem 2
x + -120 = -118.995798245

Simplifying
x + -120 = -118.995798245

Reorder the terms:
-120 + x = -118.995798245

Solving
-120 + x = -118.995798245

Solving for variable 'x'.

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

Add '120' to each side of the equation.
-120 + 120 + x = -118.995798245 + 120

Combine like terms: -120 + 120 = 0
0 + x = -118.995798245 + 120
x = -118.995798245 + 120

Combine like terms: -118.995798245 + 120 = 1.004201755
x = 1.004201755

Simplifying
x = 1.004201755


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {238.995798245, 1.004201755}
Solution
x = {238.995798245, 1.004201755}

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