480x-2x^2-100=0

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Solution for 480x-2x^2-100=0 equation: 


Simplifying
480x + -2x2 + -100 = 0

Reorder the terms:
-100 + 480x + -2x2 = 0

Solving
-100 + 480x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-50 + 240x + -1x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-50 + 240x + -1x2)' equal to zero and attempt to solve:

Simplifying
-50 + 240x + -1x2 = 0

Solving
-50 + 240x + -1x2 = 0

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

Divide each side by '-1'.
50 + -240x + x2 = 0

Move the constant term to the right:

Add '-50' to each side of the equation.
50 + -240x + -50 + x2 = 0 + -50

Reorder the terms:
50 + -50 + -240x + x2 = 0 + -50

Combine like terms: 50 + -50 = 0
0 + -240x + x2 = 0 + -50
-240x + x2 = 0 + -50

Combine like terms: 0 + -50 = -50
-240x + x2 = -50

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 = -50 + 14400

Reorder the terms:
14400 + -240x + x2 = -50 + 14400

Combine like terms: -50 + 14400 = 14350
14400 + -240x + x2 = 14350

Factor a perfect square on the left side:
(x + -120)(x + -120) = 14350

Calculate the square root of the right side: 119.791485507

Break this problem into two subproblems by setting 
(x + -120) equal to 119.791485507 and -119.791485507.


Subproblem 1
x + -120 = 119.791485507

Simplifying
x + -120 = 119.791485507

Reorder the terms:
-120 + x = 119.791485507

Solving
-120 + x = 119.791485507

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 = 119.791485507 + 120

Combine like terms: -120 + 120 = 0
0 + x = 119.791485507 + 120
x = 119.791485507 + 120

Combine like terms: 119.791485507 + 120 = 239.791485507
x = 239.791485507

Simplifying
x = 239.791485507


Subproblem 2
x + -120 = -119.791485507

Simplifying
x + -120 = -119.791485507

Reorder the terms:
-120 + x = -119.791485507

Solving
-120 + x = -119.791485507

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 = -119.791485507 + 120

Combine like terms: -120 + 120 = 0
0 + x = -119.791485507 + 120
x = -119.791485507 + 120

Combine like terms: -119.791485507 + 120 = 0.208514493
x = 0.208514493

Simplifying
x = 0.208514493


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {239.791485507, 0.208514493}
Solution
x = {239.791485507, 0.208514493}

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