41.25=(10-2x)(8-2x)

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Solution for 41.25=(10-2x)(8-2x) equation: 


Simplifying
41.25 = (10 + -2x)(8 + -2x)

Multiply (10 + -2x) * (8 + -2x)
41.25 = (10(8 + -2x) + -2x * (8 + -2x))
41.25 = ((8 * 10 + -2x * 10) + -2x * (8 + -2x))
41.25 = ((80 + -20x) + -2x * (8 + -2x))
41.25 = (80 + -20x + (8 * -2x + -2x * -2x))
41.25 = (80 + -20x + (-16x + 4x2))

Combine like terms: -20x + -16x = -36x
41.25 = (80 + -36x + 4x2)

Solving
41.25 = 80 + -36x + 4x2

Solving for variable 'x'.

Combine like terms: 41.25 + -80 = -38.75
-38.75 + 36x + -4x2 = 80 + -36x + 4x2 + -80 + 36x + -4x2

Reorder the terms:
-38.75 + 36x + -4x2 = 80 + -80 + -36x + 36x + 4x2 + -4x2

Combine like terms: 80 + -80 = 0
-38.75 + 36x + -4x2 = 0 + -36x + 36x + 4x2 + -4x2
-38.75 + 36x + -4x2 = -36x + 36x + 4x2 + -4x2

Combine like terms: -36x + 36x = 0
-38.75 + 36x + -4x2 = 0 + 4x2 + -4x2
-38.75 + 36x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-38.75 + 36x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
9.6875 + -9x + x2 = 0

Move the constant term to the right:

Add '-9.6875' to each side of the equation.
9.6875 + -9x + -9.6875 + x2 = 0 + -9.6875

Reorder the terms:
9.6875 + -9.6875 + -9x + x2 = 0 + -9.6875

Combine like terms: 9.6875 + -9.6875 = 0.0000
0.0000 + -9x + x2 = 0 + -9.6875
-9x + x2 = 0 + -9.6875

Combine like terms: 0 + -9.6875 = -9.6875
-9x + x2 = -9.6875

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = -9.6875 + 20.25

Reorder the terms:
20.25 + -9x + x2 = -9.6875 + 20.25

Combine like terms: -9.6875 + 20.25 = 10.5625
20.25 + -9x + x2 = 10.5625

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 10.5625

Calculate the square root of the right side: 3.25

Break this problem into two subproblems by setting 
(x + -4.5) equal to 3.25 and -3.25.


Subproblem 1
x + -4.5 = 3.25

Simplifying
x + -4.5 = 3.25

Reorder the terms:
-4.5 + x = 3.25

Solving
-4.5 + x = 3.25

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = 3.25 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 3.25 + 4.5
x = 3.25 + 4.5

Combine like terms: 3.25 + 4.5 = 7.75
x = 7.75

Simplifying
x = 7.75


Subproblem 2
x + -4.5 = -3.25

Simplifying
x + -4.5 = -3.25

Reorder the terms:
-4.5 + x = -3.25

Solving
-4.5 + x = -3.25

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = -3.25 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -3.25 + 4.5
x = -3.25 + 4.5

Combine like terms: -3.25 + 4.5 = 1.25
x = 1.25

Simplifying
x = 1.25


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.75, 1.25}

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