a^2+4a-2=0

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

Simplifying
a2 + 4a + -2 = 0

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

Solving
-2 + 4a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 4a + 2 + a2 = 0 + 2

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

Combine like terms: -2 + 2 = 0
0 + 4a + a2 = 0 + 2
4a + a2 = 0 + 2

Combine like terms: 0 + 2 = 2
4a + a2 = 2

The a term is 4a.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4a + 4 + a2 = 2 + 4

Reorder the terms:
4 + 4a + a2 = 2 + 4

Combine like terms: 2 + 4 = 6
4 + 4a + a2 = 6

Factor a perfect square on the left side:
(a + 2)(a + 2) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(a + 2) equal to 2.449489743 and -2.449489743.

Subproblem 1
a + 2 = 2.449489743

Simplifying
a + 2 = 2.449489743

Reorder the terms:
2 + a = 2.449489743

Solving
2 + a = 2.449489743

Solving for variable 'a'.

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

Add '-2' to each side of the equation.
2 + -2 + a = 2.449489743 + -2

Combine like terms: 2 + -2 = 0
0 + a = 2.449489743 + -2
a = 2.449489743 + -2

Combine like terms: 2.449489743 + -2 = 0.449489743
a = 0.449489743

Simplifying
a = 0.449489743

Subproblem 2
a + 2 = -2.449489743

Simplifying
a + 2 = -2.449489743

Reorder the terms:
2 + a = -2.449489743

Solving
2 + a = -2.449489743

Solving for variable 'a'.

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

Add '-2' to each side of the equation.
2 + -2 + a = -2.449489743 + -2

Combine like terms: 2 + -2 = 0
0 + a = -2.449489743 + -2
a = -2.449489743 + -2

Combine like terms: -2.449489743 + -2 = -4.449489743
a = -4.449489743

Simplifying
a = -4.449489743

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.449489743, -4.449489743}