x*x+4x-1=0

Solution for x*x+4x-1=0 equation:

Simplifying
x * x + 4x + -1 = 0

Multiply x * x
x2 + 4x + -1 = 0

Reorder the terms:
-1 + 4x + x2 = 0

Solving
-1 + 4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 4x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 4x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 4x + x2 = 0 + 1
4x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
4x + x2 = 1

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

Add '4' to each side of the equation.
4x + 4 + x2 = 1 + 4

Reorder the terms:
4 + 4x + x2 = 1 + 4

Combine like terms: 1 + 4 = 5
4 + 4x + x2 = 5

Factor a perfect square on the left side:
(x + 2)(x + 2) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(x + 2) equal to 2.236067978 and -2.236067978.

Subproblem 1
x + 2 = 2.236067978

Simplifying
x + 2 = 2.236067978

Reorder the terms:
2 + x = 2.236067978

Solving
2 + x = 2.236067978

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 2.236067978 + -2

Combine like terms: 2 + -2 = 0
0 + x = 2.236067978 + -2
x = 2.236067978 + -2

Combine like terms: 2.236067978 + -2 = 0.236067978
x = 0.236067978

Simplifying
x = 0.236067978

Subproblem 2
x + 2 = -2.236067978

Simplifying
x + 2 = -2.236067978

Reorder the terms:
2 + x = -2.236067978

Solving
2 + x = -2.236067978

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -2.236067978 + -2

Combine like terms: 2 + -2 = 0
0 + x = -2.236067978 + -2
x = -2.236067978 + -2

Combine like terms: -2.236067978 + -2 = -4.236067978
x = -4.236067978

Simplifying
x = -4.236067978

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.236067978, -4.236067978}