2(x+4)(x+4)+1=66

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Solution for 2(x+4)(x+4)+1=66 equation: 


Simplifying
2(x + 4)(x + 4) + 1 = 66

Reorder the terms:
2(4 + x)(x + 4) + 1 = 66

Reorder the terms:
2(4 + x)(4 + x) + 1 = 66

Multiply (4 + x) * (4 + x)
2(4(4 + x) + x(4 + x)) + 1 = 66
2((4 * 4 + x * 4) + x(4 + x)) + 1 = 66
2((16 + 4x) + x(4 + x)) + 1 = 66
2(16 + 4x + (4 * x + x * x)) + 1 = 66
2(16 + 4x + (4x + x2)) + 1 = 66

Combine like terms: 4x + 4x = 8x
2(16 + 8x + x2) + 1 = 66
(16 * 2 + 8x * 2 + x2 * 2) + 1 = 66
(32 + 16x + 2x2) + 1 = 66

Reorder the terms:
32 + 1 + 16x + 2x2 = 66

Combine like terms: 32 + 1 = 33
33 + 16x + 2x2 = 66

Solving
33 + 16x + 2x2 = 66

Solving for variable 'x'.

Reorder the terms:
33 + -66 + 16x + 2x2 = 66 + -66

Combine like terms: 33 + -66 = -33
-33 + 16x + 2x2 = 66 + -66

Combine like terms: 66 + -66 = 0
-33 + 16x + 2x2 = 0

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

Divide each side by '2'.
-16.5 + 8x + x2 = 0

Move the constant term to the right:

Add '16.5' to each side of the equation.
-16.5 + 8x + 16.5 + x2 = 0 + 16.5

Reorder the terms:
-16.5 + 16.5 + 8x + x2 = 0 + 16.5

Combine like terms: -16.5 + 16.5 = 0.0
0.0 + 8x + x2 = 0 + 16.5
8x + x2 = 0 + 16.5

Combine like terms: 0 + 16.5 = 16.5
8x + x2 = 16.5

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 16.5 + 16

Reorder the terms:
16 + 8x + x2 = 16.5 + 16

Combine like terms: 16.5 + 16 = 32.5
16 + 8x + x2 = 32.5

Factor a perfect square on the left side:
(x + 4)(x + 4) = 32.5

Calculate the square root of the right side: 5.700877125

Break this problem into two subproblems by setting 
(x + 4) equal to 5.700877125 and -5.700877125.


Subproblem 1
x + 4 = 5.700877125

Simplifying
x + 4 = 5.700877125

Reorder the terms:
4 + x = 5.700877125

Solving
4 + x = 5.700877125

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 5.700877125 + -4

Combine like terms: 4 + -4 = 0
0 + x = 5.700877125 + -4
x = 5.700877125 + -4

Combine like terms: 5.700877125 + -4 = 1.700877125
x = 1.700877125

Simplifying
x = 1.700877125


Subproblem 2
x + 4 = -5.700877125

Simplifying
x + 4 = -5.700877125

Reorder the terms:
4 + x = -5.700877125

Solving
4 + x = -5.700877125

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -5.700877125 + -4

Combine like terms: 4 + -4 = 0
0 + x = -5.700877125 + -4
x = -5.700877125 + -4

Combine like terms: -5.700877125 + -4 = -9.700877125
x = -9.700877125

Simplifying
x = -9.700877125


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.700877125, -9.700877125}

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