(25-2x)(15-2x)=225

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Solution for (25-2x)(15-2x)=225 equation: 


Simplifying
(25 + -2x)(15 + -2x) = 225

Multiply (25 + -2x) * (15 + -2x)
(25(15 + -2x) + -2x * (15 + -2x)) = 225
((15 * 25 + -2x * 25) + -2x * (15 + -2x)) = 225
((375 + -50x) + -2x * (15 + -2x)) = 225
(375 + -50x + (15 * -2x + -2x * -2x)) = 225
(375 + -50x + (-30x + 4x2)) = 225

Combine like terms: -50x + -30x = -80x
(375 + -80x + 4x2) = 225

Solving
375 + -80x + 4x2 = 225

Solving for variable 'x'.

Reorder the terms:
375 + -225 + -80x + 4x2 = 225 + -225

Combine like terms: 375 + -225 = 150
150 + -80x + 4x2 = 225 + -225

Combine like terms: 225 + -225 = 0
150 + -80x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(75 + -40x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(75 + -40x + 2x2)' equal to zero and attempt to solve:

Simplifying
75 + -40x + 2x2 = 0

Solving
75 + -40x + 2x2 = 0

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

Divide each side by '2'.
37.5 + -20x + x2 = 0

Move the constant term to the right:

Add '-37.5' to each side of the equation.
37.5 + -20x + -37.5 + x2 = 0 + -37.5

Reorder the terms:
37.5 + -37.5 + -20x + x2 = 0 + -37.5

Combine like terms: 37.5 + -37.5 = 0.0
0.0 + -20x + x2 = 0 + -37.5
-20x + x2 = 0 + -37.5

Combine like terms: 0 + -37.5 = -37.5
-20x + x2 = -37.5

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 = -37.5 + 100

Reorder the terms:
100 + -20x + x2 = -37.5 + 100

Combine like terms: -37.5 + 100 = 62.5
100 + -20x + x2 = 62.5

Factor a perfect square on the left side:
(x + -10)(x + -10) = 62.5

Calculate the square root of the right side: 7.90569415

Break this problem into two subproblems by setting 
(x + -10) equal to 7.90569415 and -7.90569415.


Subproblem 1
x + -10 = 7.90569415

Simplifying
x + -10 = 7.90569415

Reorder the terms:
-10 + x = 7.90569415

Solving
-10 + x = 7.90569415

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 = 7.90569415 + 10

Combine like terms: -10 + 10 = 0
0 + x = 7.90569415 + 10
x = 7.90569415 + 10

Combine like terms: 7.90569415 + 10 = 17.90569415
x = 17.90569415

Simplifying
x = 17.90569415


Subproblem 2
x + -10 = -7.90569415

Simplifying
x + -10 = -7.90569415

Reorder the terms:
-10 + x = -7.90569415

Solving
-10 + x = -7.90569415

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 = -7.90569415 + 10

Combine like terms: -10 + 10 = 0
0 + x = -7.90569415 + 10
x = -7.90569415 + 10

Combine like terms: -7.90569415 + 10 = 2.09430585
x = 2.09430585

Simplifying
x = 2.09430585


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.90569415, 2.09430585}
Solution
x = {17.90569415, 2.09430585}

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