n^2+4n-2=0

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


Simplifying
n2 + 4n + -2 = 0

Reorder the terms:
-2 + 4n + n2 = 0

Solving
-2 + 4n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 4n + 2 + n2 = 0 + 2

Reorder the terms:
-2 + 2 + 4n + n2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 4n + n2 = 0 + 2
4n + n2 = 0 + 2

Combine like terms: 0 + 2 = 2
4n + n2 = 2

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

Add '4' to each side of the equation.
4n + 4 + n2 = 2 + 4

Reorder the terms:
4 + 4n + n2 = 2 + 4

Combine like terms: 2 + 4 = 6
4 + 4n + n2 = 6

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

Calculate the square root of the right side: 2.449489743

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

Subproblem 1

n + 2 = 2.449489743 Simplifying n + 2 = 2.449489743 Reorder the terms: 2 + n = 2.449489743 Solving 2 + n = 2.449489743 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + n = 2.449489743 + -2 Combine like terms: 2 + -2 = 0 0 + n = 2.449489743 + -2 n = 2.449489743 + -2 Combine like terms: 2.449489743 + -2 = 0.449489743 n = 0.449489743 Simplifying n = 0.449489743

Subproblem 2

n + 2 = -2.449489743 Simplifying n + 2 = -2.449489743 Reorder the terms: 2 + n = -2.449489743 Solving 2 + n = -2.449489743 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + n = -2.449489743 + -2 Combine like terms: 2 + -2 = 0 0 + n = -2.449489743 + -2 n = -2.449489743 + -2 Combine like terms: -2.449489743 + -2 = -4.449489743 n = -4.449489743 Simplifying n = -4.449489743

Solution

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

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