x(20-2x)=40

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Solution for x(20-2x)=40 equation: 


Simplifying
x(20 + -2x) = 40
(20 * x + -2x * x) = 40
(20x + -2x2) = 40

Solving
20x + -2x2 = 40

Solving for variable 'x'.

Reorder the terms:
-40 + 20x + -2x2 = 40 + -40

Combine like terms: 40 + -40 = 0
-40 + 20x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-20 + 10x + -1x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-20 + 10x + -1x2)' equal to zero and attempt to solve:

Simplifying
-20 + 10x + -1x2 = 0

Solving
-20 + 10x + -1x2 = 0

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

Divide each side by '-1'.
20 + -10x + x2 = 0

Move the constant term to the right:

Add '-20' to each side of the equation.
20 + -10x + -20 + x2 = 0 + -20

Reorder the terms:
20 + -20 + -10x + x2 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -10x + x2 = 0 + -20
-10x + x2 = 0 + -20

Combine like terms: 0 + -20 = -20
-10x + x2 = -20

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 = -20 + 25

Reorder the terms:
25 + -10x + x2 = -20 + 25

Combine like terms: -20 + 25 = 5
25 + -10x + x2 = 5

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

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(x + -5) equal to 2.236067978 and -2.236067978.


Subproblem 1
x + -5 = 2.236067978

Simplifying
x + -5 = 2.236067978

Reorder the terms:
-5 + x = 2.236067978

Solving
-5 + x = 2.236067978

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 = 2.236067978 + 5

Combine like terms: -5 + 5 = 0
0 + x = 2.236067978 + 5
x = 2.236067978 + 5

Combine like terms: 2.236067978 + 5 = 7.236067978
x = 7.236067978

Simplifying
x = 7.236067978


Subproblem 2
x + -5 = -2.236067978

Simplifying
x + -5 = -2.236067978

Reorder the terms:
-5 + x = -2.236067978

Solving
-5 + x = -2.236067978

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 = -2.236067978 + 5

Combine like terms: -5 + 5 = 0
0 + x = -2.236067978 + 5
x = -2.236067978 + 5

Combine like terms: -2.236067978 + 5 = 2.763932022
x = 2.763932022

Simplifying
x = 2.763932022


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.236067978, 2.763932022}
Solution
x = {7.236067978, 2.763932022}

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