2x(4x-40)=4

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Solution for 2x(4x-40)=4 equation: 


Simplifying
2x(4x + -40) = 4

Reorder the terms:
2x(-40 + 4x) = 4
(-40 * 2x + 4x * 2x) = 4
(-80x + 8x2) = 4

Solving
-80x + 8x2 = 4

Solving for variable 'x'.

Reorder the terms:
-4 + -80x + 8x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + -80x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + -20x + 2x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-1 + -20x + 2x2)' equal to zero and attempt to solve:

Simplifying
-1 + -20x + 2x2 = 0

Solving
-1 + -20x + 2x2 = 0

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

Divide each side by '2'.
-0.5 + -10x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -10x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -10x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -10x + x2 = 0 + 0.5
-10x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-10x + x2 = 0.5

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 0.5 + 25

Reorder the terms:
25 + -10x + x2 = 0.5 + 25

Combine like terms: 0.5 + 25 = 25.5
25 + -10x + x2 = 25.5

Factor a perfect square on the left side:
(x + -5)(x + -5) = 25.5

Calculate the square root of the right side: 5.049752469

Break this problem into two subproblems by setting 
(x + -5) equal to 5.049752469 and -5.049752469.


Subproblem 1
x + -5 = 5.049752469

Simplifying
x + -5 = 5.049752469

Reorder the terms:
-5 + x = 5.049752469

Solving
-5 + x = 5.049752469

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 5.049752469 + 5

Combine like terms: -5 + 5 = 0
0 + x = 5.049752469 + 5
x = 5.049752469 + 5

Combine like terms: 5.049752469 + 5 = 10.049752469
x = 10.049752469

Simplifying
x = 10.049752469


Subproblem 2
x + -5 = -5.049752469

Simplifying
x + -5 = -5.049752469

Reorder the terms:
-5 + x = -5.049752469

Solving
-5 + x = -5.049752469

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -5.049752469 + 5

Combine like terms: -5 + 5 = 0
0 + x = -5.049752469 + 5
x = -5.049752469 + 5

Combine like terms: -5.049752469 + 5 = -0.049752469
x = -0.049752469

Simplifying
x = -0.049752469


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.049752469, -0.049752469}
Solution
x = {10.049752469, -0.049752469}

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