2a^2-1=-5a

Solution for 2a^2-1=-5a equation:

Simplifying
2a2 + -1 = -5a

Reorder the terms:
-1 + 2a2 = -5a

Solving
-1 + 2a2 = -5a

Solving for variable 'a'.

Reorder the terms:
-1 + 5a + 2a2 = -5a + 5a

Combine like terms: -5a + 5a = 0
-1 + 5a + 2a2 = 0

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

Divide each side by '2'.
-0.5 + 2.5a + a2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 2.5a + 0.5 + a2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 2.5a + a2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 2.5a + a2 = 0 + 0.5
2.5a + a2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
2.5a + a2 = 0.5

The a term is 2.5a.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5a + 1.5625 + a2 = 0.5 + 1.5625

Reorder the terms:
1.5625 + 2.5a + a2 = 0.5 + 1.5625

Combine like terms: 0.5 + 1.5625 = 2.0625
1.5625 + 2.5a + a2 = 2.0625

Factor a perfect square on the left side:
(a + 1.25)(a + 1.25) = 2.0625

Calculate the square root of the right side: 1.436140662

Break this problem into two subproblems by setting 
(a + 1.25) equal to 1.436140662 and -1.436140662.

Subproblem 1
a + 1.25 = 1.436140662

Simplifying
a + 1.25 = 1.436140662

Reorder the terms:
1.25 + a = 1.436140662

Solving
1.25 + a = 1.436140662

Solving for variable 'a'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + a = 1.436140662 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + a = 1.436140662 + -1.25
a = 1.436140662 + -1.25

Combine like terms: 1.436140662 + -1.25 = 0.186140662
a = 0.186140662

Simplifying
a = 0.186140662

Subproblem 2
a + 1.25 = -1.436140662

Simplifying
a + 1.25 = -1.436140662

Reorder the terms:
1.25 + a = -1.436140662

Solving
1.25 + a = -1.436140662

Solving for variable 'a'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + a = -1.436140662 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + a = -1.436140662 + -1.25
a = -1.436140662 + -1.25

Combine like terms: -1.436140662 + -1.25 = -2.686140662
a = -2.686140662

Simplifying
a = -2.686140662

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.186140662, -2.686140662}