2(4x+8)2x=66

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Solution for 2(4x+8)2x=66 equation: 


Simplifying
2(4x + 8) * 2x = 66

Reorder the terms:
2(8 + 4x) * 2x = 66

Reorder the terms for easier multiplication:
2 * 2x(8 + 4x) = 66

Multiply 2 * 2
4x(8 + 4x) = 66
(8 * 4x + 4x * 4x) = 66
(32x + 16x2) = 66

Solving
32x + 16x2 = 66

Solving for variable 'x'.

Reorder the terms:
-66 + 32x + 16x2 = 66 + -66

Combine like terms: 66 + -66 = 0
-66 + 32x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-33 + 16x + 8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-33 + 16x + 8x2)' equal to zero and attempt to solve:

Simplifying
-33 + 16x + 8x2 = 0

Solving
-33 + 16x + 8x2 = 0

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

Divide each side by '8'.
-4.125 + 2x + x2 = 0

Move the constant term to the right:

Add '4.125' to each side of the equation.
-4.125 + 2x + 4.125 + x2 = 0 + 4.125

Reorder the terms:
-4.125 + 4.125 + 2x + x2 = 0 + 4.125

Combine like terms: -4.125 + 4.125 = 0.000
0.000 + 2x + x2 = 0 + 4.125
2x + x2 = 0 + 4.125

Combine like terms: 0 + 4.125 = 4.125
2x + x2 = 4.125

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 4.125 + 1

Reorder the terms:
1 + 2x + x2 = 4.125 + 1

Combine like terms: 4.125 + 1 = 5.125
1 + 2x + x2 = 5.125

Factor a perfect square on the left side:
(x + 1)(x + 1) = 5.125

Calculate the square root of the right side: 2.263846285

Break this problem into two subproblems by setting 
(x + 1) equal to 2.263846285 and -2.263846285.


Subproblem 1
x + 1 = 2.263846285

Simplifying
x + 1 = 2.263846285

Reorder the terms:
1 + x = 2.263846285

Solving
1 + x = 2.263846285

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 2.263846285 + -1

Combine like terms: 1 + -1 = 0
0 + x = 2.263846285 + -1
x = 2.263846285 + -1

Combine like terms: 2.263846285 + -1 = 1.263846285
x = 1.263846285

Simplifying
x = 1.263846285


Subproblem 2
x + 1 = -2.263846285

Simplifying
x + 1 = -2.263846285

Reorder the terms:
1 + x = -2.263846285

Solving
1 + x = -2.263846285

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -2.263846285 + -1

Combine like terms: 1 + -1 = 0
0 + x = -2.263846285 + -1
x = -2.263846285 + -1

Combine like terms: -2.263846285 + -1 = -3.263846285
x = -3.263846285

Simplifying
x = -3.263846285


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.263846285, -3.263846285}
Solution
x = {1.263846285, -3.263846285}

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