n^2+4n+1=17

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Solution for n^2+4n+1=17 equation:


Simplifying
n2 + 4n + 1 = 17

Reorder the terms:
1 + 4n + n2 = 17

Solving
1 + 4n + n2 = 17

Solving for variable 'n'.

Reorder the terms:
1 + -17 + 4n + n2 = 17 + -17

Combine like terms: 1 + -17 = -16
-16 + 4n + n2 = 17 + -17

Combine like terms: 17 + -17 = 0
-16 + 4n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 4n + 16 + n2 = 0 + 16

Reorder the terms:
-16 + 16 + 4n + n2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 4n + n2 = 0 + 16
4n + n2 = 0 + 16

Combine like terms: 0 + 16 = 16
4n + n2 = 16

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 = 16 + 4

Reorder the terms:
4 + 4n + n2 = 16 + 4

Combine like terms: 16 + 4 = 20
4 + 4n + n2 = 20

Factor a perfect square on the left side:
(n + 2)(n + 2) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(n + 2) equal to 4.472135955 and -4.472135955.

Subproblem 1

n + 2 = 4.472135955 Simplifying n + 2 = 4.472135955 Reorder the terms: 2 + n = 4.472135955 Solving 2 + n = 4.472135955 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 = 4.472135955 + -2 Combine like terms: 2 + -2 = 0 0 + n = 4.472135955 + -2 n = 4.472135955 + -2 Combine like terms: 4.472135955 + -2 = 2.472135955 n = 2.472135955 Simplifying n = 2.472135955

Subproblem 2

n + 2 = -4.472135955 Simplifying n + 2 = -4.472135955 Reorder the terms: 2 + n = -4.472135955 Solving 2 + n = -4.472135955 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 = -4.472135955 + -2 Combine like terms: 2 + -2 = 0 0 + n = -4.472135955 + -2 n = -4.472135955 + -2 Combine like terms: -4.472135955 + -2 = -6.472135955 n = -6.472135955 Simplifying n = -6.472135955

Solution

The solution to the problem is based on the solutions from the subproblems. n = {2.472135955, -6.472135955}

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