0=5x^2-16x-3

Solution for 0=5x^2-16x-3 equation:

Simplifying
0 = 5x2 + -16x + -3

Reorder the terms:
0 = -3 + -16x + 5x2

Solving
0 = -3 + -16x + 5x2

Solving for variable 'x'.

Combine like terms: 0 + 3 = 3
3 + 16x + -5x2 = -3 + -16x + 5x2 + 3 + 16x + -5x2

Reorder the terms:
3 + 16x + -5x2 = -3 + 3 + -16x + 16x + 5x2 + -5x2

Combine like terms: -3 + 3 = 0
3 + 16x + -5x2 = 0 + -16x + 16x + 5x2 + -5x2
3 + 16x + -5x2 = -16x + 16x + 5x2 + -5x2

Combine like terms: -16x + 16x = 0
3 + 16x + -5x2 = 0 + 5x2 + -5x2
3 + 16x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
3 + 16x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-0.6 + -3.2x + x2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + -3.2x + 0.6 + x2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + -3.2x + x2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + -3.2x + x2 = 0 + 0.6
-3.2x + x2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
-3.2x + x2 = 0.6

The x term is -3.2x.  Take half its coefficient (-1.6).
Square it (2.56) and add it to both sides.

Add '2.56' to each side of the equation.
-3.2x + 2.56 + x2 = 0.6 + 2.56

Reorder the terms:
2.56 + -3.2x + x2 = 0.6 + 2.56

Combine like terms: 0.6 + 2.56 = 3.16
2.56 + -3.2x + x2 = 3.16

Factor a perfect square on the left side:
(x + -1.6)(x + -1.6) = 3.16

Calculate the square root of the right side: 1.777638883

Break this problem into two subproblems by setting 
(x + -1.6) equal to 1.777638883 and -1.777638883.

Subproblem 1
x + -1.6 = 1.777638883

Simplifying
x + -1.6 = 1.777638883

Reorder the terms:
-1.6 + x = 1.777638883

Solving
-1.6 + x = 1.777638883

Solving for variable 'x'.

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

Add '1.6' to each side of the equation.
-1.6 + 1.6 + x = 1.777638883 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + x = 1.777638883 + 1.6
x = 1.777638883 + 1.6

Combine like terms: 1.777638883 + 1.6 = 3.377638883
x = 3.377638883

Simplifying
x = 3.377638883

Subproblem 2
x + -1.6 = -1.777638883

Simplifying
x + -1.6 = -1.777638883

Reorder the terms:
-1.6 + x = -1.777638883

Solving
-1.6 + x = -1.777638883

Solving for variable 'x'.

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

Add '1.6' to each side of the equation.
-1.6 + 1.6 + x = -1.777638883 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + x = -1.777638883 + 1.6
x = -1.777638883 + 1.6

Combine like terms: -1.777638883 + 1.6 = -0.177638883
x = -0.177638883

Simplifying
x = -0.177638883

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.377638883, -0.177638883}