1=x(20-2x)

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Solution for 1=x(20-2x) equation:


Simplifying
1 = x(20 + -2x)
1 = (20 * x + -2x * x)
1 = (20x + -2x2)

Solving
1 = 20x + -2x2

Solving for variable 'x'.

Reorder the terms:
1 + -20x + 2x2 = 20x + -20x + -2x2 + 2x2

Combine like terms: 20x + -20x = 0
1 + -20x + 2x2 = 0 + -2x2 + 2x2
1 + -20x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
1 + -20x + 2x2 = 0

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

Divide each side by '2'.
0.5 + -10x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -10x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -10x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -10x + x2 = 0 + -0.5
-10x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-10x + x2 = -0.5

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = -0.5 + 25

Reorder the terms:
25 + -10x + x2 = -0.5 + 25

Combine like terms: -0.5 + 25 = 24.5
25 + -10x + x2 = 24.5

Factor a perfect square on the left side:
(x + -5)(x + -5) = 24.5

Calculate the square root of the right side: 4.949747468

Break this problem into two subproblems by setting 
(x + -5) equal to 4.949747468 and -4.949747468.

Subproblem 1

x + -5 = 4.949747468 Simplifying x + -5 = 4.949747468 Reorder the terms: -5 + x = 4.949747468 Solving -5 + x = 4.949747468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 4.949747468 + 5 Combine like terms: -5 + 5 = 0 0 + x = 4.949747468 + 5 x = 4.949747468 + 5 Combine like terms: 4.949747468 + 5 = 9.949747468 x = 9.949747468 Simplifying x = 9.949747468

Subproblem 2

x + -5 = -4.949747468 Simplifying x + -5 = -4.949747468 Reorder the terms: -5 + x = -4.949747468 Solving -5 + x = -4.949747468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -4.949747468 + 5 Combine like terms: -5 + 5 = 0 0 + x = -4.949747468 + 5 x = -4.949747468 + 5 Combine like terms: -4.949747468 + 5 = 0.050252532 x = 0.050252532 Simplifying x = 0.050252532

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.949747468, 0.050252532}

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