5x^2+16x-5=0

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

Simplifying
5x2 + 16x + -5 = 0

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

Solving
-5 + 16x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
-1 + 3.2x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 3.2x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 3.2x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 3.2x + x2 = 0 + 1
3.2x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
3.2x + x2 = 1

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 = 1 + 2.56

Reorder the terms:
2.56 + 3.2x + x2 = 1 + 2.56

Combine like terms: 1 + 2.56 = 3.56
2.56 + 3.2x + x2 = 3.56

Factor a perfect square on the left side:
(x + 1.6)(x + 1.6) = 3.56

Calculate the square root of the right side: 1.886796226

Break this problem into two subproblems by setting 
(x + 1.6) equal to 1.886796226 and -1.886796226.

Subproblem 1
x + 1.6 = 1.886796226

Simplifying
x + 1.6 = 1.886796226

Reorder the terms:
1.6 + x = 1.886796226

Solving
1.6 + x = 1.886796226

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 = 1.886796226 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + x = 1.886796226 + -1.6
x = 1.886796226 + -1.6

Combine like terms: 1.886796226 + -1.6 = 0.286796226
x = 0.286796226

Simplifying
x = 0.286796226

Subproblem 2
x + 1.6 = -1.886796226

Simplifying
x + 1.6 = -1.886796226

Reorder the terms:
1.6 + x = -1.886796226

Solving
1.6 + x = -1.886796226

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 = -1.886796226 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + x = -1.886796226 + -1.6
x = -1.886796226 + -1.6

Combine like terms: -1.886796226 + -1.6 = -3.486796226
x = -3.486796226

Simplifying
x = -3.486796226

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.286796226, -3.486796226}