-5(1-5x)*5(-8x-2)=-4x-8x

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Solution for -5(1-5x)*5(-8x-2)=-4x-8x equation:


Simplifying
-5(1 + -5x) * 5(-8x + -2) = -4x + -8x

Reorder the terms:
-5(1 + -5x) * 5(-2 + -8x) = -4x + -8x

Reorder the terms for easier multiplication:
-5 * 5(1 + -5x)(-2 + -8x) = -4x + -8x

Multiply -5 * 5
-25(1 + -5x)(-2 + -8x) = -4x + -8x

Multiply (1 + -5x) * (-2 + -8x)
-25(1(-2 + -8x) + -5x * (-2 + -8x)) = -4x + -8x
-25((-2 * 1 + -8x * 1) + -5x * (-2 + -8x)) = -4x + -8x
-25((-2 + -8x) + -5x * (-2 + -8x)) = -4x + -8x
-25(-2 + -8x + (-2 * -5x + -8x * -5x)) = -4x + -8x
-25(-2 + -8x + (10x + 40x2)) = -4x + -8x

Combine like terms: -8x + 10x = 2x
-25(-2 + 2x + 40x2) = -4x + -8x
(-2 * -25 + 2x * -25 + 40x2 * -25) = -4x + -8x
(50 + -50x + -1000x2) = -4x + -8x

Combine like terms: -4x + -8x = -12x
50 + -50x + -1000x2 = -12x

Solving
50 + -50x + -1000x2 = -12x

Solving for variable 'x'.

Reorder the terms:
50 + -50x + 12x + -1000x2 = -12x + 12x

Combine like terms: -50x + 12x = -38x
50 + -38x + -1000x2 = -12x + 12x

Combine like terms: -12x + 12x = 0
50 + -38x + -1000x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(25 + -19x + -500x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(25 + -19x + -500x2)' equal to zero and attempt to solve:

Simplifying
25 + -19x + -500x2 = 0

Solving
25 + -19x + -500x2 = 0

Begin completing the square.  Divide all terms by
-500 the coefficient of the squared term: 

Divide each side by '-500'.
-0.05 + 0.038x + x2 = 0.00

Move the constant term to the right:

Add '0.05' to each side of the equation.
-0.05 + 0.038x + 0.05 + x2 = 0.00 + 0.05

Reorder the terms:
-0.05 + 0.05 + 0.038x + x2 = 0.00 + 0.05

Combine like terms: -0.05 + 0.05 = 0.00
0.00 + 0.038x + x2 = 0.00 + 0.05
0.038x + x2 = 0.00 + 0.05

Combine like terms: 0.00 + 0.05 = 0.05
0.038x + x2 = 0.05

The x term is 0.038x.  Take half its coefficient (0.019).
Square it (0.000361) and add it to both sides.

Add '0.000361' to each side of the equation.
0.038x + 0.000361 + x2 = 0.05 + 0.000361

Reorder the terms:
0.000361 + 0.038x + x2 = 0.05 + 0.000361

Combine like terms: 0.05 + 0.000361 = 0.050361
0.000361 + 0.038x + x2 = 0.050361

Factor a perfect square on the left side:
(x + 0.019)(x + 0.019) = 0.050361

Calculate the square root of the right side: 0.224412566

Break this problem into two subproblems by setting 
(x + 0.019) equal to 0.224412566 and -0.224412566.


Subproblem 1
x + 0.019 = 0.224412566

Simplifying
x + 0.019 = 0.224412566

Reorder the terms:
0.019 + x = 0.224412566

Solving
0.019 + x = 0.224412566

Solving for variable 'x'.

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

Add '-0.019' to each side of the equation.
0.019 + -0.019 + x = 0.224412566 + -0.019

Combine like terms: 0.019 + -0.019 = 0.000
0.000 + x = 0.224412566 + -0.019
x = 0.224412566 + -0.019

Combine like terms: 0.224412566 + -0.019 = 0.205412566
x = 0.205412566

Simplifying
x = 0.205412566


Subproblem 2
x + 0.019 = -0.224412566

Simplifying
x + 0.019 = -0.224412566

Reorder the terms:
0.019 + x = -0.224412566

Solving
0.019 + x = -0.224412566

Solving for variable 'x'.

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

Add '-0.019' to each side of the equation.
0.019 + -0.019 + x = -0.224412566 + -0.019

Combine like terms: 0.019 + -0.019 = 0.000
0.000 + x = -0.224412566 + -0.019
x = -0.224412566 + -0.019

Combine like terms: -0.224412566 + -0.019 = -0.243412566
x = -0.243412566

Simplifying
x = -0.243412566


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.205412566, -0.243412566}
Solution
x = {0.205412566, -0.243412566}

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