x(20-x)=20

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


Simplifying
x(20 + -1x) = 20
(20 * x + -1x * x) = 20
(20x + -1x2) = 20

Solving
20x + -1x2 = 20

Solving for variable 'x'.

Reorder the terms:
-20 + 20x + -1x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + 20x + -1x2 = 0

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

Divide each side by '-1'.
20 + -20x + x2 = 0

Move the constant term to the right:

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

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

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

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

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 = -20 + 100

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

Combine like terms: -20 + 100 = 80
100 + -20x + x2 = 80

Factor a perfect square on the left side:
(x + -10)(x + -10) = 80

Calculate the square root of the right side: 8.94427191

Break this problem into two subproblems by setting 
(x + -10) equal to 8.94427191 and -8.94427191.

Subproblem 1

x + -10 = 8.94427191 Simplifying x + -10 = 8.94427191 Reorder the terms: -10 + x = 8.94427191 Solving -10 + x = 8.94427191 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 = 8.94427191 + 10 Combine like terms: -10 + 10 = 0 0 + x = 8.94427191 + 10 x = 8.94427191 + 10 Combine like terms: 8.94427191 + 10 = 18.94427191 x = 18.94427191 Simplifying x = 18.94427191

Subproblem 2

x + -10 = -8.94427191 Simplifying x + -10 = -8.94427191 Reorder the terms: -10 + x = -8.94427191 Solving -10 + x = -8.94427191 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 = -8.94427191 + 10 Combine like terms: -10 + 10 = 0 0 + x = -8.94427191 + 10 x = -8.94427191 + 10 Combine like terms: -8.94427191 + 10 = 1.05572809 x = 1.05572809 Simplifying x = 1.05572809

Solution

The solution to the problem is based on the solutions from the subproblems. x = {18.94427191, 1.05572809}

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