x^2+16x+4=0

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Solution for x^2+16x+4=0 equation: 


Simplifying
x2 + 16x + 4 = 0

Reorder the terms:
4 + 16x + x2 = 0

Solving
4 + 16x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 16x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + 16x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 16x + x2 = 0 + -4
16x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
16x + x2 = -4

The x term is 16x.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16x + 64 + x2 = -4 + 64

Reorder the terms:
64 + 16x + x2 = -4 + 64

Combine like terms: -4 + 64 = 60
64 + 16x + x2 = 60

Factor a perfect square on the left side:
(x + 8)(x + 8) = 60

Calculate the square root of the right side: 7.745966692

Break this problem into two subproblems by setting 
(x + 8) equal to 7.745966692 and -7.745966692.


Subproblem 1
x + 8 = 7.745966692

Simplifying
x + 8 = 7.745966692

Reorder the terms:
8 + x = 7.745966692

Solving
8 + x = 7.745966692

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = 7.745966692 + -8

Combine like terms: 8 + -8 = 0
0 + x = 7.745966692 + -8
x = 7.745966692 + -8

Combine like terms: 7.745966692 + -8 = -0.254033308
x = -0.254033308

Simplifying
x = -0.254033308


Subproblem 2
x + 8 = -7.745966692

Simplifying
x + 8 = -7.745966692

Reorder the terms:
8 + x = -7.745966692

Solving
8 + x = -7.745966692

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = -7.745966692 + -8

Combine like terms: 8 + -8 = 0
0 + x = -7.745966692 + -8
x = -7.745966692 + -8

Combine like terms: -7.745966692 + -8 = -15.745966692
x = -15.745966692

Simplifying
x = -15.745966692


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.254033308, -15.745966692}

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