100=3x(20-x)

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Solution for 100=3x(20-x) equation:


Simplifying
100 = 3x(20 + -1x)
100 = (20 * 3x + -1x * 3x)
100 = (60x + -3x2)

Solving
100 = 60x + -3x2

Solving for variable 'x'.

Reorder the terms:
100 + -60x + 3x2 = 60x + -60x + -3x2 + 3x2

Combine like terms: 60x + -60x = 0
100 + -60x + 3x2 = 0 + -3x2 + 3x2
100 + -60x + 3x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
100 + -60x + 3x2 = 0

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

Divide each side by '3'.
33.33333333 + -20x + x2 = 0

Move the constant term to the right:

Add '-33.33333333' to each side of the equation.
33.33333333 + -20x + -33.33333333 + x2 = 0 + -33.33333333

Reorder the terms:
33.33333333 + -33.33333333 + -20x + x2 = 0 + -33.33333333

Combine like terms: 33.33333333 + -33.33333333 = 0.00000000
0.00000000 + -20x + x2 = 0 + -33.33333333
-20x + x2 = 0 + -33.33333333

Combine like terms: 0 + -33.33333333 = -33.33333333
-20x + x2 = -33.33333333

The x term is -20x.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x + 100 + x2 = -33.33333333 + 100

Reorder the terms:
100 + -20x + x2 = -33.33333333 + 100

Combine like terms: -33.33333333 + 100 = 66.66666667
100 + -20x + x2 = 66.66666667

Factor a perfect square on the left side:
(x + -10)(x + -10) = 66.66666667

Calculate the square root of the right side: 8.164965809

Break this problem into two subproblems by setting 
(x + -10) equal to 8.164965809 and -8.164965809.

Subproblem 1

x + -10 = 8.164965809 Simplifying x + -10 = 8.164965809 Reorder the terms: -10 + x = 8.164965809 Solving -10 + x = 8.164965809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 8.164965809 + 10 Combine like terms: -10 + 10 = 0 0 + x = 8.164965809 + 10 x = 8.164965809 + 10 Combine like terms: 8.164965809 + 10 = 18.164965809 x = 18.164965809 Simplifying x = 18.164965809

Subproblem 2

x + -10 = -8.164965809 Simplifying x + -10 = -8.164965809 Reorder the terms: -10 + x = -8.164965809 Solving -10 + x = -8.164965809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -8.164965809 + 10 Combine like terms: -10 + 10 = 0 0 + x = -8.164965809 + 10 x = -8.164965809 + 10 Combine like terms: -8.164965809 + 10 = 1.835034191 x = 1.835034191 Simplifying x = 1.835034191

Solution

The solution to the problem is based on the solutions from the subproblems. x = {18.164965809, 1.835034191}

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