0=x^2+4x-2

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


Simplifying
0 = x2 + 4x + -2

Reorder the terms:
0 = -2 + 4x + x2

Solving
0 = -2 + 4x + x2

Solving for variable 'x'.

Combine like terms: 0 + 2 = 2
2 + -4x + -1x2 = -2 + 4x + x2 + 2 + -4x + -1x2

Reorder the terms:
2 + -4x + -1x2 = -2 + 2 + 4x + -4x + x2 + -1x2

Combine like terms: -2 + 2 = 0
2 + -4x + -1x2 = 0 + 4x + -4x + x2 + -1x2
2 + -4x + -1x2 = 4x + -4x + x2 + -1x2

Combine like terms: 4x + -4x = 0
2 + -4x + -1x2 = 0 + x2 + -1x2
2 + -4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
2 + -4x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-2 + 4x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 4x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 4x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 4x + x2 = 0 + 2
4x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
4x + x2 = 2

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 = 2 + 4

Reorder the terms:
4 + 4x + x2 = 2 + 4

Combine like terms: 2 + 4 = 6
4 + 4x + x2 = 6

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

Calculate the square root of the right side: 2.449489743

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


Subproblem 1
x + 2 = 2.449489743

Simplifying
x + 2 = 2.449489743

Reorder the terms:
2 + x = 2.449489743

Solving
2 + x = 2.449489743

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 = 2.449489743 + -2

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

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

Simplifying
x = 0.449489743


Subproblem 2
x + 2 = -2.449489743

Simplifying
x + 2 = -2.449489743

Reorder the terms:
2 + x = -2.449489743

Solving
2 + x = -2.449489743

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 = -2.449489743 + -2

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

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

Simplifying
x = -4.449489743


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

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