2x^2+16x-3=0

Solution for 2x^2+16x-3=0 equation:

Simplifying
2x2 + 16x + -3 = 0

Reorder the terms:
-3 + 16x + 2x2 = 0

Solving
-3 + 16x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-1.5 + 8x + x2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 8x + 1.5 + x2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 8x + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 8x + x2 = 0 + 1.5
8x + x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
8x + x2 = 1.5

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 = 1.5 + 16

Reorder the terms:
16 + 8x + x2 = 1.5 + 16

Combine like terms: 1.5 + 16 = 17.5
16 + 8x + x2 = 17.5

Factor a perfect square on the left side:
(x + 4)(x + 4) = 17.5

Calculate the square root of the right side: 4.183300133

Break this problem into two subproblems by setting 
(x + 4) equal to 4.183300133 and -4.183300133.

Subproblem 1
x + 4 = 4.183300133

Simplifying
x + 4 = 4.183300133

Reorder the terms:
4 + x = 4.183300133

Solving
4 + x = 4.183300133

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 = 4.183300133 + -4

Combine like terms: 4 + -4 = 0
0 + x = 4.183300133 + -4
x = 4.183300133 + -4

Combine like terms: 4.183300133 + -4 = 0.183300133
x = 0.183300133

Simplifying
x = 0.183300133

Subproblem 2
x + 4 = -4.183300133

Simplifying
x + 4 = -4.183300133

Reorder the terms:
4 + x = -4.183300133

Solving
4 + x = -4.183300133

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 = -4.183300133 + -4

Combine like terms: 4 + -4 = 0
0 + x = -4.183300133 + -4
x = -4.183300133 + -4

Combine like terms: -4.183300133 + -4 = -8.183300133
x = -8.183300133

Simplifying
x = -8.183300133

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.183300133, -8.183300133}