(10-2x)(8-2x)=38.75

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Solution for (10-2x)(8-2x)=38.75 equation:


Simplifying
(10 + -2x)(8 + -2x) = 38.75

Multiply (10 + -2x) * (8 + -2x)
(10(8 + -2x) + -2x * (8 + -2x)) = 38.75
((8 * 10 + -2x * 10) + -2x * (8 + -2x)) = 38.75
((80 + -20x) + -2x * (8 + -2x)) = 38.75
(80 + -20x + (8 * -2x + -2x * -2x)) = 38.75
(80 + -20x + (-16x + 4x2)) = 38.75

Combine like terms: -20x + -16x = -36x
(80 + -36x + 4x2) = 38.75

Solving
80 + -36x + 4x2 = 38.75

Solving for variable 'x'.

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

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

Combine like terms: 38.75 + -38.75 = 0.00
41.25 + -36x + 4x2 = 0.00

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

Divide each side by '4'.
10.3125 + -9x + x2 = 0.00

Move the constant term to the right:

Add '-10.3125' to each side of the equation.
10.3125 + -9x + -10.3125 + x2 = 0.00 + -10.3125

Reorder the terms:
10.3125 + -10.3125 + -9x + x2 = 0.00 + -10.3125

Combine like terms: 10.3125 + -10.3125 = 0.0000
0.0000 + -9x + x2 = 0.00 + -10.3125
-9x + x2 = 0.00 + -10.3125

Combine like terms: 0.00 + -10.3125 = -10.3125
-9x + x2 = -10.3125

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 = -10.3125 + 20.25

Reorder the terms:
20.25 + -9x + x2 = -10.3125 + 20.25

Combine like terms: -10.3125 + 20.25 = 9.9375
20.25 + -9x + x2 = 9.9375

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 9.9375

Calculate the square root of the right side: 3.152380053

Break this problem into two subproblems by setting 
(x + -4.5) equal to 3.152380053 and -3.152380053.

Subproblem 1

x + -4.5 = 3.152380053 Simplifying x + -4.5 = 3.152380053 Reorder the terms: -4.5 + x = 3.152380053 Solving -4.5 + x = 3.152380053 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 = 3.152380053 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 3.152380053 + 4.5 x = 3.152380053 + 4.5 Combine like terms: 3.152380053 + 4.5 = 7.652380053 x = 7.652380053 Simplifying x = 7.652380053

Subproblem 2

x + -4.5 = -3.152380053 Simplifying x + -4.5 = -3.152380053 Reorder the terms: -4.5 + x = -3.152380053 Solving -4.5 + x = -3.152380053 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 = -3.152380053 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -3.152380053 + 4.5 x = -3.152380053 + 4.5 Combine like terms: -3.152380053 + 4.5 = 1.347619947 x = 1.347619947 Simplifying x = 1.347619947

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.652380053, 1.347619947}

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