5200=n(20-0.1n)+100

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Solution for 5200=n(20-0.1n)+100 equation: 


Simplifying
5200 = n(20 + -0.1n) + 100
5200 = (20 * n + -0.1n * n) + 100
5200 = (20n + -0.1n2) + 100

Reorder the terms:
5200 = 100 + 20n + -0.1n2

Solving
5200 = 100 + 20n + -0.1n2

Solving for variable 'n'.

Combine like terms: 5200 + -100 = 5100
5100 + -20n + 0.1n2 = 100 + 20n + -0.1n2 + -100 + -20n + 0.1n2

Reorder the terms:
5100 + -20n + 0.1n2 = 100 + -100 + 20n + -20n + -0.1n2 + 0.1n2

Combine like terms: 100 + -100 = 0
5100 + -20n + 0.1n2 = 0 + 20n + -20n + -0.1n2 + 0.1n2
5100 + -20n + 0.1n2 = 20n + -20n + -0.1n2 + 0.1n2

Combine like terms: 20n + -20n = 0
5100 + -20n + 0.1n2 = 0 + -0.1n2 + 0.1n2
5100 + -20n + 0.1n2 = -0.1n2 + 0.1n2

Combine like terms: -0.1n2 + 0.1n2 = 0.0
5100 + -20n + 0.1n2 = 0.0

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

Divide each side by '0.1'.
51000 + -200n + n2 = 0

Move the constant term to the right:

Add '-51000' to each side of the equation.
51000 + -200n + -51000 + n2 = 0 + -51000

Reorder the terms:
51000 + -51000 + -200n + n2 = 0 + -51000

Combine like terms: 51000 + -51000 = 0
0 + -200n + n2 = 0 + -51000
-200n + n2 = 0 + -51000

Combine like terms: 0 + -51000 = -51000
-200n + n2 = -51000

The n term is -200n.  Take half its coefficient (-100).
Square it (10000) and add it to both sides.

Add '10000' to each side of the equation.
-200n + 10000 + n2 = -51000 + 10000

Reorder the terms:
10000 + -200n + n2 = -51000 + 10000

Combine like terms: -51000 + 10000 = -41000
10000 + -200n + n2 = -41000

Factor a perfect square on the left side:
(n + -100)(n + -100) = -41000

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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