n^2-2n-16=0

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Solution for n^2-2n-16=0 equation:


Simplifying
n2 + -2n + -16 = 0

Reorder the terms:
-16 + -2n + n2 = 0

Solving
-16 + -2n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -2n + 16 + n2 = 0 + 16

Reorder the terms:
-16 + 16 + -2n + n2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -2n + n2 = 0 + 16
-2n + n2 = 0 + 16

Combine like terms: 0 + 16 = 16
-2n + n2 = 16

The n term is -2n.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2n + 1 + n2 = 16 + 1

Reorder the terms:
1 + -2n + n2 = 16 + 1

Combine like terms: 16 + 1 = 17
1 + -2n + n2 = 17

Factor a perfect square on the left side:
(n + -1)(n + -1) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(n + -1) equal to 4.123105626 and -4.123105626.

Subproblem 1

n + -1 = 4.123105626 Simplifying n + -1 = 4.123105626 Reorder the terms: -1 + n = 4.123105626 Solving -1 + n = 4.123105626 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + n = 4.123105626 + 1 Combine like terms: -1 + 1 = 0 0 + n = 4.123105626 + 1 n = 4.123105626 + 1 Combine like terms: 4.123105626 + 1 = 5.123105626 n = 5.123105626 Simplifying n = 5.123105626

Subproblem 2

n + -1 = -4.123105626 Simplifying n + -1 = -4.123105626 Reorder the terms: -1 + n = -4.123105626 Solving -1 + n = -4.123105626 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + n = -4.123105626 + 1 Combine like terms: -1 + 1 = 0 0 + n = -4.123105626 + 1 n = -4.123105626 + 1 Combine like terms: -4.123105626 + 1 = -3.123105626 n = -3.123105626 Simplifying n = -3.123105626

Solution

The solution to the problem is based on the solutions from the subproblems. n = {5.123105626, -3.123105626}

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