(40-2x)(20-2x)=784

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Solution for (40-2x)(20-2x)=784 equation: 


Simplifying
(40 + -2x)(20 + -2x) = 784

Multiply (40 + -2x) * (20 + -2x)
(40(20 + -2x) + -2x * (20 + -2x)) = 784
((20 * 40 + -2x * 40) + -2x * (20 + -2x)) = 784
((800 + -80x) + -2x * (20 + -2x)) = 784
(800 + -80x + (20 * -2x + -2x * -2x)) = 784
(800 + -80x + (-40x + 4x2)) = 784

Combine like terms: -80x + -40x = -120x
(800 + -120x + 4x2) = 784

Solving
800 + -120x + 4x2 = 784

Solving for variable 'x'.

Reorder the terms:
800 + -784 + -120x + 4x2 = 784 + -784

Combine like terms: 800 + -784 = 16
16 + -120x + 4x2 = 784 + -784

Combine like terms: 784 + -784 = 0
16 + -120x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(4 + -30x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(4 + -30x + x2)' equal to zero and attempt to solve:

Simplifying
4 + -30x + x2 = 0

Solving
4 + -30x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -30x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -30x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -30x + x2 = 0 + -4
-30x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-30x + x2 = -4

The x term is -30x.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30x + 225 + x2 = -4 + 225

Reorder the terms:
225 + -30x + x2 = -4 + 225

Combine like terms: -4 + 225 = 221
225 + -30x + x2 = 221

Factor a perfect square on the left side:
(x + -15)(x + -15) = 221

Calculate the square root of the right side: 14.866068747

Break this problem into two subproblems by setting 
(x + -15) equal to 14.866068747 and -14.866068747.


Subproblem 1
x + -15 = 14.866068747

Simplifying
x + -15 = 14.866068747

Reorder the terms:
-15 + x = 14.866068747

Solving
-15 + x = 14.866068747

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + x = 14.866068747 + 15

Combine like terms: -15 + 15 = 0
0 + x = 14.866068747 + 15
x = 14.866068747 + 15

Combine like terms: 14.866068747 + 15 = 29.866068747
x = 29.866068747

Simplifying
x = 29.866068747


Subproblem 2
x + -15 = -14.866068747

Simplifying
x + -15 = -14.866068747

Reorder the terms:
-15 + x = -14.866068747

Solving
-15 + x = -14.866068747

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + x = -14.866068747 + 15

Combine like terms: -15 + 15 = 0
0 + x = -14.866068747 + 15
x = -14.866068747 + 15

Combine like terms: -14.866068747 + 15 = 0.133931253
x = 0.133931253

Simplifying
x = 0.133931253


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {29.866068747, 0.133931253}
Solution
x = {29.866068747, 0.133931253}

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