5a^2+31a+28=0

Solution for 5a^2+31a+28=0 equation:

Simplifying
5a2 + 31a + 28 = 0

Reorder the terms:
28 + 31a + 5a2 = 0

Solving
28 + 31a + 5a2 = 0

Solving for variable 'a'.

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

Divide each side by '5'.
5.6 + 6.2a + a2 = 0

Move the constant term to the right:

Add '-5.6' to each side of the equation.
5.6 + 6.2a + -5.6 + a2 = 0 + -5.6

Reorder the terms:
5.6 + -5.6 + 6.2a + a2 = 0 + -5.6

Combine like terms: 5.6 + -5.6 = 0.0
0.0 + 6.2a + a2 = 0 + -5.6
6.2a + a2 = 0 + -5.6

Combine like terms: 0 + -5.6 = -5.6
6.2a + a2 = -5.6

The a term is 6.2a.  Take half its coefficient (3.1).
Square it (9.61) and add it to both sides.

Add '9.61' to each side of the equation.
6.2a + 9.61 + a2 = -5.6 + 9.61

Reorder the terms:
9.61 + 6.2a + a2 = -5.6 + 9.61

Combine like terms: -5.6 + 9.61 = 4.01
9.61 + 6.2a + a2 = 4.01

Factor a perfect square on the left side:
(a + 3.1)(a + 3.1) = 4.01

Calculate the square root of the right side: 2.002498439

Break this problem into two subproblems by setting 
(a + 3.1) equal to 2.002498439 and -2.002498439.

Subproblem 1
a + 3.1 = 2.002498439

Simplifying
a + 3.1 = 2.002498439

Reorder the terms:
3.1 + a = 2.002498439

Solving
3.1 + a = 2.002498439

Solving for variable 'a'.

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

Add '-3.1' to each side of the equation.
3.1 + -3.1 + a = 2.002498439 + -3.1

Combine like terms: 3.1 + -3.1 = 0.0
0.0 + a = 2.002498439 + -3.1
a = 2.002498439 + -3.1

Combine like terms: 2.002498439 + -3.1 = -1.097501561
a = -1.097501561

Simplifying
a = -1.097501561

Subproblem 2
a + 3.1 = -2.002498439

Simplifying
a + 3.1 = -2.002498439

Reorder the terms:
3.1 + a = -2.002498439

Solving
3.1 + a = -2.002498439

Solving for variable 'a'.

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

Add '-3.1' to each side of the equation.
3.1 + -3.1 + a = -2.002498439 + -3.1

Combine like terms: 3.1 + -3.1 = 0.0
0.0 + a = -2.002498439 + -3.1
a = -2.002498439 + -3.1

Combine like terms: -2.002498439 + -3.1 = -5.102498439
a = -5.102498439

Simplifying
a = -5.102498439

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {-1.097501561, -5.102498439}