x^2+(-4x-14)(-4x-14)=25

Solution for x^2+(-4x-14)(-4x-14)=25 equation:

Simplifying
x2 + (-4x + -14)(-4x + -14) = 25

Reorder the terms:
x2 + (-14 + -4x)(-4x + -14) = 25

Reorder the terms:
x2 + (-14 + -4x)(-14 + -4x) = 25

Multiply (-14 + -4x) * (-14 + -4x)
x2 + (-14(-14 + -4x) + -4x * (-14 + -4x)) = 25
x2 + ((-14 * -14 + -4x * -14) + -4x * (-14 + -4x)) = 25
x2 + ((196 + 56x) + -4x * (-14 + -4x)) = 25
x2 + (196 + 56x + (-14 * -4x + -4x * -4x)) = 25
x2 + (196 + 56x + (56x + 16x2)) = 25

Combine like terms: 56x + 56x = 112x
x2 + (196 + 112x + 16x2) = 25

Reorder the terms:
196 + 112x + x2 + 16x2 = 25

Combine like terms: x2 + 16x2 = 17x2
196 + 112x + 17x2 = 25

Solving
196 + 112x + 17x2 = 25

Solving for variable 'x'.

Reorder the terms:
196 + -25 + 112x + 17x2 = 25 + -25

Combine like terms: 196 + -25 = 171
171 + 112x + 17x2 = 25 + -25

Combine like terms: 25 + -25 = 0
171 + 112x + 17x2 = 0

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

Divide each side by '17'.
10.05882353 + 6.588235294x + x2 = 0

Move the constant term to the right:

Add '-10.05882353' to each side of the equation.
10.05882353 + 6.588235294x + -10.05882353 + x2 = 0 + -10.05882353

Reorder the terms:
10.05882353 + -10.05882353 + 6.588235294x + x2 = 0 + -10.05882353

Combine like terms: 10.05882353 + -10.05882353 = 0.00000000
0.00000000 + 6.588235294x + x2 = 0 + -10.05882353
6.588235294x + x2 = 0 + -10.05882353

Combine like terms: 0 + -10.05882353 = -10.05882353
6.588235294x + x2 = -10.05882353

The x term is 6.588235294x.  Take half its coefficient (3.294117647).
Square it (10.85121107) and add it to both sides.

Add '10.85121107' to each side of the equation.
6.588235294x + 10.85121107 + x2 = -10.05882353 + 10.85121107

Reorder the terms:
10.85121107 + 6.588235294x + x2 = -10.05882353 + 10.85121107

Combine like terms: -10.05882353 + 10.85121107 = 0.79238754
10.85121107 + 6.588235294x + x2 = 0.79238754

Factor a perfect square on the left side:
(x + 3.294117647)(x + 3.294117647) = 0.79238754

Calculate the square root of the right side: 0.890161525

Break this problem into two subproblems by setting 
(x + 3.294117647) equal to 0.890161525 and -0.890161525.

Subproblem 1
x + 3.294117647 = 0.890161525

Simplifying
x + 3.294117647 = 0.890161525

Reorder the terms:
3.294117647 + x = 0.890161525

Solving
3.294117647 + x = 0.890161525

Solving for variable 'x'.

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

Add '-3.294117647' to each side of the equation.
3.294117647 + -3.294117647 + x = 0.890161525 + -3.294117647

Combine like terms: 3.294117647 + -3.294117647 = 0.000000000
0.000000000 + x = 0.890161525 + -3.294117647
x = 0.890161525 + -3.294117647

Combine like terms: 0.890161525 + -3.294117647 = -2.403956122
x = -2.403956122

Simplifying
x = -2.403956122

Subproblem 2
x + 3.294117647 = -0.890161525

Simplifying
x + 3.294117647 = -0.890161525

Reorder the terms:
3.294117647 + x = -0.890161525

Solving
3.294117647 + x = -0.890161525

Solving for variable 'x'.

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

Add '-3.294117647' to each side of the equation.
3.294117647 + -3.294117647 + x = -0.890161525 + -3.294117647

Combine like terms: 3.294117647 + -3.294117647 = 0.000000000
0.000000000 + x = -0.890161525 + -3.294117647
x = -0.890161525 + -3.294117647

Combine like terms: -0.890161525 + -3.294117647 = -4.184279172
x = -4.184279172

Simplifying
x = -4.184279172

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.403956122, -4.184279172}