2a^2+4a-1=0

Solution for 2a^2+4a-1=0 equation:

Simplifying
2a2 + 4a + -1 = 0

Reorder the terms:
-1 + 4a + 2a2 = 0

Solving
-1 + 4a + 2a2 = 0

Solving for variable 'a'.

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

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

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 2a + 0.5 + a2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 2a + a2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 2a + a2 = 0 + 0.5
2a + a2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
2a + a2 = 0.5

The a term is 2a.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2a + 1 + a2 = 0.5 + 1

Reorder the terms:
1 + 2a + a2 = 0.5 + 1

Combine like terms: 0.5 + 1 = 1.5
1 + 2a + a2 = 1.5

Factor a perfect square on the left side:
(a + 1)(a + 1) = 1.5

Calculate the square root of the right side: 1.224744871

Break this problem into two subproblems by setting 
(a + 1) equal to 1.224744871 and -1.224744871.

Subproblem 1
a + 1 = 1.224744871

Simplifying
a + 1 = 1.224744871

Reorder the terms:
1 + a = 1.224744871

Solving
1 + a = 1.224744871

Solving for variable 'a'.

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

Add '-1' to each side of the equation.
1 + -1 + a = 1.224744871 + -1

Combine like terms: 1 + -1 = 0
0 + a = 1.224744871 + -1
a = 1.224744871 + -1

Combine like terms: 1.224744871 + -1 = 0.224744871
a = 0.224744871

Simplifying
a = 0.224744871

Subproblem 2
a + 1 = -1.224744871

Simplifying
a + 1 = -1.224744871

Reorder the terms:
1 + a = -1.224744871

Solving
1 + a = -1.224744871

Solving for variable 'a'.

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

Add '-1' to each side of the equation.
1 + -1 + a = -1.224744871 + -1

Combine like terms: 1 + -1 = 0
0 + a = -1.224744871 + -1
a = -1.224744871 + -1

Combine like terms: -1.224744871 + -1 = -2.224744871
a = -2.224744871

Simplifying
a = -2.224744871

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.224744871, -2.224744871}