2x^2+16x=-1

Solution for 2x^2+16x=-1 equation:

Simplifying
2x2 + 16x = -1

Reorder the terms:
16x + 2x2 = -1

Solving
16x + 2x2 = -1

Solving for variable 'x'.

Reorder the terms:
1 + 16x + 2x2 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + 16x + 2x2 = 0

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

Divide each side by '2'.
0.5 + 8x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 8x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 8x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 8x + x2 = 0 + -0.5
8x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
8x + x2 = -0.5

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 = -0.5 + 16

Reorder the terms:
16 + 8x + x2 = -0.5 + 16

Combine like terms: -0.5 + 16 = 15.5
16 + 8x + x2 = 15.5

Factor a perfect square on the left side:
(x + 4)(x + 4) = 15.5

Calculate the square root of the right side: 3.937003937

Break this problem into two subproblems by setting 
(x + 4) equal to 3.937003937 and -3.937003937.

Subproblem 1
x + 4 = 3.937003937

Simplifying
x + 4 = 3.937003937

Reorder the terms:
4 + x = 3.937003937

Solving
4 + x = 3.937003937

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 = 3.937003937 + -4

Combine like terms: 4 + -4 = 0
0 + x = 3.937003937 + -4
x = 3.937003937 + -4

Combine like terms: 3.937003937 + -4 = -0.062996063
x = -0.062996063

Simplifying
x = -0.062996063

Subproblem 2
x + 4 = -3.937003937

Simplifying
x + 4 = -3.937003937

Reorder the terms:
4 + x = -3.937003937

Solving
4 + x = -3.937003937

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 = -3.937003937 + -4

Combine like terms: 4 + -4 = 0
0 + x = -3.937003937 + -4
x = -3.937003937 + -4

Combine like terms: -3.937003937 + -4 = -7.937003937
x = -7.937003937

Simplifying
x = -7.937003937

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.062996063, -7.937003937}