5500=2x(120-x)

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Solution for 5500=2x(120-x) equation: 


Simplifying
5500 = 2x(120 + -1x)
5500 = (120 * 2x + -1x * 2x)
5500 = (240x + -2x2)

Solving
5500 = 240x + -2x2

Solving for variable 'x'.

Reorder the terms:
5500 + -240x + 2x2 = 240x + -240x + -2x2 + 2x2

Combine like terms: 240x + -240x = 0
5500 + -240x + 2x2 = 0 + -2x2 + 2x2
5500 + -240x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
5500 + -240x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(2750 + -120x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(2750 + -120x + x2)' equal to zero and attempt to solve:

Simplifying
2750 + -120x + x2 = 0

Solving
2750 + -120x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2750' to each side of the equation.
2750 + -120x + -2750 + x2 = 0 + -2750

Reorder the terms:
2750 + -2750 + -120x + x2 = 0 + -2750

Combine like terms: 2750 + -2750 = 0
0 + -120x + x2 = 0 + -2750
-120x + x2 = 0 + -2750

Combine like terms: 0 + -2750 = -2750
-120x + x2 = -2750

The x term is -120x.  Take half its coefficient (-60).
Square it (3600) and add it to both sides.

Add '3600' to each side of the equation.
-120x + 3600 + x2 = -2750 + 3600

Reorder the terms:
3600 + -120x + x2 = -2750 + 3600

Combine like terms: -2750 + 3600 = 850
3600 + -120x + x2 = 850

Factor a perfect square on the left side:
(x + -60)(x + -60) = 850

Calculate the square root of the right side: 29.154759474

Break this problem into two subproblems by setting 
(x + -60) equal to 29.154759474 and -29.154759474.


Subproblem 1
x + -60 = 29.154759474

Simplifying
x + -60 = 29.154759474

Reorder the terms:
-60 + x = 29.154759474

Solving
-60 + x = 29.154759474

Solving for variable 'x'.

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

Add '60' to each side of the equation.
-60 + 60 + x = 29.154759474 + 60

Combine like terms: -60 + 60 = 0
0 + x = 29.154759474 + 60
x = 29.154759474 + 60

Combine like terms: 29.154759474 + 60 = 89.154759474
x = 89.154759474

Simplifying
x = 89.154759474


Subproblem 2
x + -60 = -29.154759474

Simplifying
x + -60 = -29.154759474

Reorder the terms:
-60 + x = -29.154759474

Solving
-60 + x = -29.154759474

Solving for variable 'x'.

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

Add '60' to each side of the equation.
-60 + 60 + x = -29.154759474 + 60

Combine like terms: -60 + 60 = 0
0 + x = -29.154759474 + 60
x = -29.154759474 + 60

Combine like terms: -29.154759474 + 60 = 30.845240526
x = 30.845240526

Simplifying
x = 30.845240526


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {89.154759474, 30.845240526}
Solution
x = {89.154759474, 30.845240526}

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