5a^2-13a=16

Solution for 5a^2-13a=16 equation:

Simplifying
5a2 + -13a = 16

Reorder the terms:
-13a + 5a2 = 16

Solving
-13a + 5a2 = 16

Solving for variable 'a'.

Reorder the terms:
-16 + -13a + 5a2 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + -13a + 5a2 = 0

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

Divide each side by '5'.
-3.2 + -2.6a + a2 = 0

Move the constant term to the right:

Add '3.2' to each side of the equation.
-3.2 + -2.6a + 3.2 + a2 = 0 + 3.2

Reorder the terms:
-3.2 + 3.2 + -2.6a + a2 = 0 + 3.2

Combine like terms: -3.2 + 3.2 = 0.0
0.0 + -2.6a + a2 = 0 + 3.2
-2.6a + a2 = 0 + 3.2

Combine like terms: 0 + 3.2 = 3.2
-2.6a + a2 = 3.2

The a term is -2.6a.  Take half its coefficient (-1.3).
Square it (1.69) and add it to both sides.

Add '1.69' to each side of the equation.
-2.6a + 1.69 + a2 = 3.2 + 1.69

Reorder the terms:
1.69 + -2.6a + a2 = 3.2 + 1.69

Combine like terms: 3.2 + 1.69 = 4.89
1.69 + -2.6a + a2 = 4.89

Factor a perfect square on the left side:
(a + -1.3)(a + -1.3) = 4.89

Calculate the square root of the right side: 2.211334439

Break this problem into two subproblems by setting 
(a + -1.3) equal to 2.211334439 and -2.211334439.

Subproblem 1
a + -1.3 = 2.211334439

Simplifying
a + -1.3 = 2.211334439

Reorder the terms:
-1.3 + a = 2.211334439

Solving
-1.3 + a = 2.211334439

Solving for variable 'a'.

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

Add '1.3' to each side of the equation.
-1.3 + 1.3 + a = 2.211334439 + 1.3

Combine like terms: -1.3 + 1.3 = 0.0
0.0 + a = 2.211334439 + 1.3
a = 2.211334439 + 1.3

Combine like terms: 2.211334439 + 1.3 = 3.511334439
a = 3.511334439

Simplifying
a = 3.511334439

Subproblem 2
a + -1.3 = -2.211334439

Simplifying
a + -1.3 = -2.211334439

Reorder the terms:
-1.3 + a = -2.211334439

Solving
-1.3 + a = -2.211334439

Solving for variable 'a'.

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

Add '1.3' to each side of the equation.
-1.3 + 1.3 + a = -2.211334439 + 1.3

Combine like terms: -1.3 + 1.3 = 0.0
0.0 + a = -2.211334439 + 1.3
a = -2.211334439 + 1.3

Combine like terms: -2.211334439 + 1.3 = -0.911334439
a = -0.911334439

Simplifying
a = -0.911334439

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {3.511334439, -0.911334439}