2(x+7)(x+7)=64

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Solution for 2(x+7)(x+7)=64 equation: 


Simplifying
2(x + 7)(x + 7) = 64

Reorder the terms:
2(7 + x)(x + 7) = 64

Reorder the terms:
2(7 + x)(7 + x) = 64

Multiply (7 + x) * (7 + x)
2(7(7 + x) + x(7 + x)) = 64
2((7 * 7 + x * 7) + x(7 + x)) = 64
2((49 + 7x) + x(7 + x)) = 64
2(49 + 7x + (7 * x + x * x)) = 64
2(49 + 7x + (7x + x2)) = 64

Combine like terms: 7x + 7x = 14x
2(49 + 14x + x2) = 64
(49 * 2 + 14x * 2 + x2 * 2) = 64
(98 + 28x + 2x2) = 64

Solving
98 + 28x + 2x2 = 64

Solving for variable 'x'.

Reorder the terms:
98 + -64 + 28x + 2x2 = 64 + -64

Combine like terms: 98 + -64 = 34
34 + 28x + 2x2 = 64 + -64

Combine like terms: 64 + -64 = 0
34 + 28x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(17 + 14x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(17 + 14x + x2)' equal to zero and attempt to solve:

Simplifying
17 + 14x + x2 = 0

Solving
17 + 14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-17' to each side of the equation.
17 + 14x + -17 + x2 = 0 + -17

Reorder the terms:
17 + -17 + 14x + x2 = 0 + -17

Combine like terms: 17 + -17 = 0
0 + 14x + x2 = 0 + -17
14x + x2 = 0 + -17

Combine like terms: 0 + -17 = -17
14x + x2 = -17

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = -17 + 49

Reorder the terms:
49 + 14x + x2 = -17 + 49

Combine like terms: -17 + 49 = 32
49 + 14x + x2 = 32

Factor a perfect square on the left side:
(x + 7)(x + 7) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(x + 7) equal to 5.656854249 and -5.656854249.


Subproblem 1
x + 7 = 5.656854249

Simplifying
x + 7 = 5.656854249

Reorder the terms:
7 + x = 5.656854249

Solving
7 + x = 5.656854249

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = 5.656854249 + -7

Combine like terms: 7 + -7 = 0
0 + x = 5.656854249 + -7
x = 5.656854249 + -7

Combine like terms: 5.656854249 + -7 = -1.343145751
x = -1.343145751

Simplifying
x = -1.343145751


Subproblem 2
x + 7 = -5.656854249

Simplifying
x + 7 = -5.656854249

Reorder the terms:
7 + x = -5.656854249

Solving
7 + x = -5.656854249

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = -5.656854249 + -7

Combine like terms: 7 + -7 = 0
0 + x = -5.656854249 + -7
x = -5.656854249 + -7

Combine like terms: -5.656854249 + -7 = -12.656854249
x = -12.656854249

Simplifying
x = -12.656854249


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.343145751, -12.656854249}
Solution
x = {-1.343145751, -12.656854249}

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