40-(5-2x)(8-2x)=10

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Solution for 40-(5-2x)(8-2x)=10 equation: 


Simplifying
40 + -1(5 + -2x)(8 + -2x) = 10

Multiply (5 + -2x) * (8 + -2x)
40 + -1(5(8 + -2x) + -2x * (8 + -2x)) = 10
40 + -1((8 * 5 + -2x * 5) + -2x * (8 + -2x)) = 10
40 + -1((40 + -10x) + -2x * (8 + -2x)) = 10
40 + -1(40 + -10x + (8 * -2x + -2x * -2x)) = 10
40 + -1(40 + -10x + (-16x + 4x2)) = 10

Combine like terms: -10x + -16x = -26x
40 + -1(40 + -26x + 4x2) = 10
40 + (40 * -1 + -26x * -1 + 4x2 * -1) = 10
40 + (-40 + 26x + -4x2) = 10

Combine like terms: 40 + -40 = 0
0 + 26x + -4x2 = 10
26x + -4x2 = 10

Solving
26x + -4x2 = 10

Solving for variable 'x'.

Reorder the terms:
-10 + 26x + -4x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 26x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 13x + -2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + 13x + -2x2)' equal to zero and attempt to solve:

Simplifying
-5 + 13x + -2x2 = 0

Solving
-5 + 13x + -2x2 = 0

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

Divide each side by '-2'.
2.5 + -6.5x + x2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + -6.5x + -2.5 + x2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + -6.5x + x2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + -6.5x + x2 = 0 + -2.5
-6.5x + x2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
-6.5x + x2 = -2.5

The x term is -6.5x.  Take half its coefficient (-3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
-6.5x + 10.5625 + x2 = -2.5 + 10.5625

Reorder the terms:
10.5625 + -6.5x + x2 = -2.5 + 10.5625

Combine like terms: -2.5 + 10.5625 = 8.0625
10.5625 + -6.5x + x2 = 8.0625

Factor a perfect square on the left side:
(x + -3.25)(x + -3.25) = 8.0625

Calculate the square root of the right side: 2.839454173

Break this problem into two subproblems by setting 
(x + -3.25) equal to 2.839454173 and -2.839454173.


Subproblem 1
x + -3.25 = 2.839454173

Simplifying
x + -3.25 = 2.839454173

Reorder the terms:
-3.25 + x = 2.839454173

Solving
-3.25 + x = 2.839454173

Solving for variable 'x'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + x = 2.839454173 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + x = 2.839454173 + 3.25
x = 2.839454173 + 3.25

Combine like terms: 2.839454173 + 3.25 = 6.089454173
x = 6.089454173

Simplifying
x = 6.089454173


Subproblem 2
x + -3.25 = -2.839454173

Simplifying
x + -3.25 = -2.839454173

Reorder the terms:
-3.25 + x = -2.839454173

Solving
-3.25 + x = -2.839454173

Solving for variable 'x'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + x = -2.839454173 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + x = -2.839454173 + 3.25
x = -2.839454173 + 3.25

Combine like terms: -2.839454173 + 3.25 = 0.410545827
x = 0.410545827

Simplifying
x = 0.410545827


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.089454173, 0.410545827}
Solution
x = {6.089454173, 0.410545827}

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