10a^2+8a-16=0

Solution for 10a^2+8a-16=0 equation:

Simplifying
10a2 + 8a + -16 = 0

Reorder the terms:
-16 + 8a + 10a2 = 0

Solving
-16 + 8a + 10a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + 4a + 5a2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-8 + 4a + 5a2)' equal to zero and attempt to solve:

Simplifying
-8 + 4a + 5a2 = 0

Solving
-8 + 4a + 5a2 = 0

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

Divide each side by '5'.
-1.6 + 0.8a + a2 = 0

Move the constant term to the right:

Add '1.6' to each side of the equation.
-1.6 + 0.8a + 1.6 + a2 = 0 + 1.6

Reorder the terms:
-1.6 + 1.6 + 0.8a + a2 = 0 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + 0.8a + a2 = 0 + 1.6
0.8a + a2 = 0 + 1.6

Combine like terms: 0 + 1.6 = 1.6
0.8a + a2 = 1.6

The a term is 0.8a.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8a + 0.16 + a2 = 1.6 + 0.16

Reorder the terms:
0.16 + 0.8a + a2 = 1.6 + 0.16

Combine like terms: 1.6 + 0.16 = 1.76
0.16 + 0.8a + a2 = 1.76

Factor a perfect square on the left side:
(a + 0.4)(a + 0.4) = 1.76

Calculate the square root of the right side: 1.326649916

Break this problem into two subproblems by setting 
(a + 0.4) equal to 1.326649916 and -1.326649916.

Subproblem 1
a + 0.4 = 1.326649916

Simplifying
a + 0.4 = 1.326649916

Reorder the terms:
0.4 + a = 1.326649916

Solving
0.4 + a = 1.326649916

Solving for variable 'a'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + a = 1.326649916 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + a = 1.326649916 + -0.4
a = 1.326649916 + -0.4

Combine like terms: 1.326649916 + -0.4 = 0.926649916
a = 0.926649916

Simplifying
a = 0.926649916

Subproblem 2
a + 0.4 = -1.326649916

Simplifying
a + 0.4 = -1.326649916

Reorder the terms:
0.4 + a = -1.326649916

Solving
0.4 + a = -1.326649916

Solving for variable 'a'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + a = -1.326649916 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + a = -1.326649916 + -0.4
a = -1.326649916 + -0.4

Combine like terms: -1.326649916 + -0.4 = -1.726649916
a = -1.726649916

Simplifying
a = -1.726649916

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.926649916, -1.726649916}
Solution
a = {0.926649916, -1.726649916}