5x^2+16x-13=0

Solution for 5x^2+16x-13=0 equation:

Simplifying
5x2 + 16x + -13 = 0

Reorder the terms:
-13 + 16x + 5x2 = 0

Solving
-13 + 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'.
-2.6 + 3.2x + x2 = 0

Move the constant term to the right:

Add '2.6' to each side of the equation.
-2.6 + 3.2x + 2.6 + x2 = 0 + 2.6

Reorder the terms:
-2.6 + 2.6 + 3.2x + x2 = 0 + 2.6

Combine like terms: -2.6 + 2.6 = 0.0
0.0 + 3.2x + x2 = 0 + 2.6
3.2x + x2 = 0 + 2.6

Combine like terms: 0 + 2.6 = 2.6
3.2x + x2 = 2.6

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 = 2.6 + 2.56

Reorder the terms:
2.56 + 3.2x + x2 = 2.6 + 2.56

Combine like terms: 2.6 + 2.56 = 5.16
2.56 + 3.2x + x2 = 5.16

Factor a perfect square on the left side:
(x + 1.6)(x + 1.6) = 5.16

Calculate the square root of the right side: 2.271563338

Break this problem into two subproblems by setting 
(x + 1.6) equal to 2.271563338 and -2.271563338.

Subproblem 1
x + 1.6 = 2.271563338

Simplifying
x + 1.6 = 2.271563338

Reorder the terms:
1.6 + x = 2.271563338

Solving
1.6 + x = 2.271563338

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 = 2.271563338 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + x = 2.271563338 + -1.6
x = 2.271563338 + -1.6

Combine like terms: 2.271563338 + -1.6 = 0.671563338
x = 0.671563338

Simplifying
x = 0.671563338

Subproblem 2
x + 1.6 = -2.271563338

Simplifying
x + 1.6 = -2.271563338

Reorder the terms:
1.6 + x = -2.271563338

Solving
1.6 + x = -2.271563338

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 = -2.271563338 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + x = -2.271563338 + -1.6
x = -2.271563338 + -1.6

Combine like terms: -2.271563338 + -1.6 = -3.871563338
x = -3.871563338

Simplifying
x = -3.871563338

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.671563338, -3.871563338}