n^2-17n+18=0

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Solution for n^2-17n+18=0 equation: 


Simplifying
n2 + -17n + 18 = 0

Reorder the terms:
18 + -17n + n2 = 0

Solving
18 + -17n + 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 + -17n + -18 + n2 = 0 + -18

Reorder the terms:
18 + -18 + -17n + n2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -17n + n2 = 0 + -18
-17n + n2 = 0 + -18

Combine like terms: 0 + -18 = -18
-17n + n2 = -18

The n term is -17n.  Take half its coefficient (-8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
-17n + 72.25 + n2 = -18 + 72.25

Reorder the terms:
72.25 + -17n + n2 = -18 + 72.25

Combine like terms: -18 + 72.25 = 54.25
72.25 + -17n + n2 = 54.25

Factor a perfect square on the left side:
(n + -8.5)(n + -8.5) = 54.25

Calculate the square root of the right side: 7.365459931

Break this problem into two subproblems by setting 
(n + -8.5) equal to 7.365459931 and -7.365459931.


Subproblem 1
n + -8.5 = 7.365459931

Simplifying
n + -8.5 = 7.365459931

Reorder the terms:
-8.5 + n = 7.365459931

Solving
-8.5 + n = 7.365459931

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '8.5' to each side of the equation.
-8.5 + 8.5 + n = 7.365459931 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + n = 7.365459931 + 8.5
n = 7.365459931 + 8.5

Combine like terms: 7.365459931 + 8.5 = 15.865459931
n = 15.865459931

Simplifying
n = 15.865459931


Subproblem 2
n + -8.5 = -7.365459931

Simplifying
n + -8.5 = -7.365459931

Reorder the terms:
-8.5 + n = -7.365459931

Solving
-8.5 + n = -7.365459931

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '8.5' to each side of the equation.
-8.5 + 8.5 + n = -7.365459931 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + n = -7.365459931 + 8.5
n = -7.365459931 + 8.5

Combine like terms: -7.365459931 + 8.5 = 1.134540069
n = 1.134540069

Simplifying
n = 1.134540069


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {15.865459931, 1.134540069}

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