5a^2+16a-12=-1

Solution for 5a^2+16a-12=-1 equation:

Simplifying
5a2 + 16a + -12 = -1

Reorder the terms:
-12 + 16a + 5a2 = -1

Solving
-12 + 16a + 5a2 = -1

Solving for variable 'a'.

Reorder the terms:
-12 + 1 + 16a + 5a2 = -1 + 1

Combine like terms: -12 + 1 = -11
-11 + 16a + 5a2 = -1 + 1

Combine like terms: -1 + 1 = 0
-11 + 16a + 5a2 = 0

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

Divide each side by '5'.
-2.2 + 3.2a + a2 = 0

Move the constant term to the right:

Add '2.2' to each side of the equation.
-2.2 + 3.2a + 2.2 + a2 = 0 + 2.2

Reorder the terms:
-2.2 + 2.2 + 3.2a + a2 = 0 + 2.2

Combine like terms: -2.2 + 2.2 = 0.0
0.0 + 3.2a + a2 = 0 + 2.2
3.2a + a2 = 0 + 2.2

Combine like terms: 0 + 2.2 = 2.2
3.2a + a2 = 2.2

The a term is 3.2a.  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.
3.2a + 2.56 + a2 = 2.2 + 2.56

Reorder the terms:
2.56 + 3.2a + a2 = 2.2 + 2.56

Combine like terms: 2.2 + 2.56 = 4.76
2.56 + 3.2a + a2 = 4.76

Factor a perfect square on the left side:
(a + 1.6)(a + 1.6) = 4.76

Calculate the square root of the right side: 2.181742423

Break this problem into two subproblems by setting 
(a + 1.6) equal to 2.181742423 and -2.181742423.

Subproblem 1
a + 1.6 = 2.181742423

Simplifying
a + 1.6 = 2.181742423

Reorder the terms:
1.6 + a = 2.181742423

Solving
1.6 + a = 2.181742423

Solving for variable 'a'.

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

Add '-1.6' to each side of the equation.
1.6 + -1.6 + a = 2.181742423 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + a = 2.181742423 + -1.6
a = 2.181742423 + -1.6

Combine like terms: 2.181742423 + -1.6 = 0.581742423
a = 0.581742423

Simplifying
a = 0.581742423

Subproblem 2
a + 1.6 = -2.181742423

Simplifying
a + 1.6 = -2.181742423

Reorder the terms:
1.6 + a = -2.181742423

Solving
1.6 + a = -2.181742423

Solving for variable 'a'.

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

Add '-1.6' to each side of the equation.
1.6 + -1.6 + a = -2.181742423 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + a = -2.181742423 + -1.6
a = -2.181742423 + -1.6

Combine like terms: -2.181742423 + -1.6 = -3.781742423
a = -3.781742423

Simplifying
a = -3.781742423

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.581742423, -3.781742423}