n^2+2n-18=0

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Solution for n^2+2n-18=0 equation:


Simplifying
n2 + 2n + -18 = 0

Reorder the terms:
-18 + 2n + n2 = 0

Solving
-18 + 2n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + 2n + 18 + n2 = 0 + 18

Reorder the terms:
-18 + 18 + 2n + n2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + 2n + n2 = 0 + 18
2n + n2 = 0 + 18

Combine like terms: 0 + 18 = 18
2n + n2 = 18

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 = 18 + 1

Reorder the terms:
1 + 2n + n2 = 18 + 1

Combine like terms: 18 + 1 = 19
1 + 2n + n2 = 19

Factor a perfect square on the left side:
(n + 1)(n + 1) = 19

Calculate the square root of the right side: 4.358898944

Break this problem into two subproblems by setting 
(n + 1) equal to 4.358898944 and -4.358898944.

Subproblem 1

n + 1 = 4.358898944 Simplifying n + 1 = 4.358898944 Reorder the terms: 1 + n = 4.358898944 Solving 1 + n = 4.358898944 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 = 4.358898944 + -1 Combine like terms: 1 + -1 = 0 0 + n = 4.358898944 + -1 n = 4.358898944 + -1 Combine like terms: 4.358898944 + -1 = 3.358898944 n = 3.358898944 Simplifying n = 3.358898944

Subproblem 2

n + 1 = -4.358898944 Simplifying n + 1 = -4.358898944 Reorder the terms: 1 + n = -4.358898944 Solving 1 + n = -4.358898944 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 = -4.358898944 + -1 Combine like terms: 1 + -1 = 0 0 + n = -4.358898944 + -1 n = -4.358898944 + -1 Combine like terms: -4.358898944 + -1 = -5.358898944 n = -5.358898944 Simplifying n = -5.358898944

Solution

The solution to the problem is based on the solutions from the subproblems. n = {3.358898944, -5.358898944}

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