2x[4x-1]=42

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Solution for 2x[4x-1]=42 equation: 


Simplifying
2x[4x + -1] = 42

Reorder the terms:
2x[-1 + 4x] = 42
[-1 * 2x + 4x * 2x] = 42
[-2x + 8x2] = 42

Solving
-2x + 8x2 = 42

Solving for variable 'x'.

Reorder the terms:
-42 + -2x + 8x2 = 42 + -42

Combine like terms: 42 + -42 = 0
-42 + -2x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + -1x + 4x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-21 + -1x + 4x2)' equal to zero and attempt to solve:

Simplifying
-21 + -1x + 4x2 = 0

Solving
-21 + -1x + 4x2 = 0

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

Divide each side by '4'.
-5.25 + -0.25x + x2 = 0

Move the constant term to the right:

Add '5.25' to each side of the equation.
-5.25 + -0.25x + 5.25 + x2 = 0 + 5.25

Reorder the terms:
-5.25 + 5.25 + -0.25x + x2 = 0 + 5.25

Combine like terms: -5.25 + 5.25 = 0.00
0.00 + -0.25x + x2 = 0 + 5.25
-0.25x + x2 = 0 + 5.25

Combine like terms: 0 + 5.25 = 5.25
-0.25x + x2 = 5.25

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 = 5.25 + 0.015625

Reorder the terms:
0.015625 + -0.25x + x2 = 5.25 + 0.015625

Combine like terms: 5.25 + 0.015625 = 5.265625
0.015625 + -0.25x + x2 = 5.265625

Factor a perfect square on the left side:
(x + -0.125)(x + -0.125) = 5.265625

Calculate the square root of the right side: 2.294694969

Break this problem into two subproblems by setting 
(x + -0.125) equal to 2.294694969 and -2.294694969.


Subproblem 1
x + -0.125 = 2.294694969

Simplifying
x + -0.125 = 2.294694969

Reorder the terms:
-0.125 + x = 2.294694969

Solving
-0.125 + x = 2.294694969

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 = 2.294694969 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + x = 2.294694969 + 0.125
x = 2.294694969 + 0.125

Combine like terms: 2.294694969 + 0.125 = 2.419694969
x = 2.419694969

Simplifying
x = 2.419694969


Subproblem 2
x + -0.125 = -2.294694969

Simplifying
x + -0.125 = -2.294694969

Reorder the terms:
-0.125 + x = -2.294694969

Solving
-0.125 + x = -2.294694969

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 = -2.294694969 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + x = -2.294694969 + 0.125
x = -2.294694969 + 0.125

Combine like terms: -2.294694969 + 0.125 = -2.169694969
x = -2.169694969

Simplifying
x = -2.169694969


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.419694969, -2.169694969}
Solution
x = {2.419694969, -2.169694969}

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