-4a^2-8=a

Solution for -4a^2-8=a equation:

Simplifying
-4a2 + -8 = a

Reorder the terms:
-8 + -4a2 = a

Solving
-8 + -4a2 = a

Solving for variable 'a'.

Reorder the terms:
-8 + -1a + -4a2 = a + -1a

Combine like terms: a + -1a = 0
-8 + -1a + -4a2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(8 + a + 4a2) = 0

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

Simplifying
8 + a + 4a2 = 0

Solving
8 + a + 4a2 = 0

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

Divide each side by '4'.
2 + 0.25a + a2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 0.25a + -2 + a2 = 0 + -2

Reorder the terms:
2 + -2 + 0.25a + a2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 0.25a + a2 = 0 + -2
0.25a + a2 = 0 + -2

Combine like terms: 0 + -2 = -2
0.25a + a2 = -2

The a term is a.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.25a + 0.25 + a2 = -2 + 0.25

Reorder the terms:
0.25 + 0.25a + a2 = -2 + 0.25

Combine like terms: -2 + 0.25 = -1.75
0.25 + 0.25a + a2 = -1.75

Factor a perfect square on the left side:
(a + 0.5)(a + 0.5) = -1.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.