5x(8x-2)=130

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Solution for 5x(8x-2)=130 equation: 


Simplifying
5x(8x + -2) = 130

Reorder the terms:
5x(-2 + 8x) = 130
(-2 * 5x + 8x * 5x) = 130
(-10x + 40x2) = 130

Solving
-10x + 40x2 = 130

Solving for variable 'x'.

Reorder the terms:
-130 + -10x + 40x2 = 130 + -130

Combine like terms: 130 + -130 = 0
-130 + -10x + 40x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-13 + -1x + 4x2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(-13 + -1x + 4x2)' equal to zero and attempt to solve:

Simplifying
-13 + -1x + 4x2 = 0

Solving
-13 + -1x + 4x2 = 0

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

Divide each side by '4'.
-3.25 + -0.25x + x2 = 0

Move the constant term to the right:

Add '3.25' to each side of the equation.
-3.25 + -0.25x + 3.25 + x2 = 0 + 3.25

Reorder the terms:
-3.25 + 3.25 + -0.25x + x2 = 0 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + -0.25x + x2 = 0 + 3.25
-0.25x + x2 = 0 + 3.25

Combine like terms: 0 + 3.25 = 3.25
-0.25x + x2 = 3.25

The x term is -0.25x.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25x + 0.015625 + x2 = 3.25 + 0.015625

Reorder the terms:
0.015625 + -0.25x + x2 = 3.25 + 0.015625

Combine like terms: 3.25 + 0.015625 = 3.265625
0.015625 + -0.25x + x2 = 3.265625

Factor a perfect square on the left side:
(x + -0.125)(x + -0.125) = 3.265625

Calculate the square root of the right side: 1.807104037

Break this problem into two subproblems by setting 
(x + -0.125) equal to 1.807104037 and -1.807104037.


Subproblem 1
x + -0.125 = 1.807104037

Simplifying
x + -0.125 = 1.807104037

Reorder the terms:
-0.125 + x = 1.807104037

Solving
-0.125 + x = 1.807104037

Solving for variable 'x'.

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

Add '0.125' to each side of the equation.
-0.125 + 0.125 + x = 1.807104037 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + x = 1.807104037 + 0.125
x = 1.807104037 + 0.125

Combine like terms: 1.807104037 + 0.125 = 1.932104037
x = 1.932104037

Simplifying
x = 1.932104037


Subproblem 2
x + -0.125 = -1.807104037

Simplifying
x + -0.125 = -1.807104037

Reorder the terms:
-0.125 + x = -1.807104037

Solving
-0.125 + x = -1.807104037

Solving for variable 'x'.

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

Add '0.125' to each side of the equation.
-0.125 + 0.125 + x = -1.807104037 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + x = -1.807104037 + 0.125
x = -1.807104037 + 0.125

Combine like terms: -1.807104037 + 0.125 = -1.682104037
x = -1.682104037

Simplifying
x = -1.682104037


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.932104037, -1.682104037}
Solution
x = {1.932104037, -1.682104037}

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