(40-2x)(60-2x)=2000

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Solution for (40-2x)(60-2x)=2000 equation: 


Simplifying
(40 + -2x)(60 + -2x) = 2000

Multiply (40 + -2x) * (60 + -2x)
(40(60 + -2x) + -2x * (60 + -2x)) = 2000
((60 * 40 + -2x * 40) + -2x * (60 + -2x)) = 2000
((2400 + -80x) + -2x * (60 + -2x)) = 2000
(2400 + -80x + (60 * -2x + -2x * -2x)) = 2000
(2400 + -80x + (-120x + 4x2)) = 2000

Combine like terms: -80x + -120x = -200x
(2400 + -200x + 4x2) = 2000

Solving
2400 + -200x + 4x2 = 2000

Solving for variable 'x'.

Reorder the terms:
2400 + -2000 + -200x + 4x2 = 2000 + -2000

Combine like terms: 2400 + -2000 = 400
400 + -200x + 4x2 = 2000 + -2000

Combine like terms: 2000 + -2000 = 0
400 + -200x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(100 + -50x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(100 + -50x + x2)' equal to zero and attempt to solve:

Simplifying
100 + -50x + x2 = 0

Solving
100 + -50x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-100' to each side of the equation.
100 + -50x + -100 + x2 = 0 + -100

Reorder the terms:
100 + -100 + -50x + x2 = 0 + -100

Combine like terms: 100 + -100 = 0
0 + -50x + x2 = 0 + -100
-50x + x2 = 0 + -100

Combine like terms: 0 + -100 = -100
-50x + x2 = -100

The x term is -50x.  Take half its coefficient (-25).
Square it (625) and add it to both sides.

Add '625' to each side of the equation.
-50x + 625 + x2 = -100 + 625

Reorder the terms:
625 + -50x + x2 = -100 + 625

Combine like terms: -100 + 625 = 525
625 + -50x + x2 = 525

Factor a perfect square on the left side:
(x + -25)(x + -25) = 525

Calculate the square root of the right side: 22.912878475

Break this problem into two subproblems by setting 
(x + -25) equal to 22.912878475 and -22.912878475.


Subproblem 1
x + -25 = 22.912878475

Simplifying
x + -25 = 22.912878475

Reorder the terms:
-25 + x = 22.912878475

Solving
-25 + x = 22.912878475

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '25' to each side of the equation.
-25 + 25 + x = 22.912878475 + 25

Combine like terms: -25 + 25 = 0
0 + x = 22.912878475 + 25
x = 22.912878475 + 25

Combine like terms: 22.912878475 + 25 = 47.912878475
x = 47.912878475

Simplifying
x = 47.912878475


Subproblem 2
x + -25 = -22.912878475

Simplifying
x + -25 = -22.912878475

Reorder the terms:
-25 + x = -22.912878475

Solving
-25 + x = -22.912878475

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '25' to each side of the equation.
-25 + 25 + x = -22.912878475 + 25

Combine like terms: -25 + 25 = 0
0 + x = -22.912878475 + 25
x = -22.912878475 + 25

Combine like terms: -22.912878475 + 25 = 2.087121525
x = 2.087121525

Simplifying
x = 2.087121525


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {47.912878475, 2.087121525}
Solution
x = {47.912878475, 2.087121525}

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