n^2-8n+9=0

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Solution for n^2-8n+9=0 equation:


Simplifying
n2 + -8n + 9 = 0

Reorder the terms:
9 + -8n + n2 = 0

Solving
9 + -8n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + -8n + -9 + n2 = 0 + -9

Reorder the terms:
9 + -9 + -8n + n2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -8n + n2 = 0 + -9
-8n + n2 = 0 + -9

Combine like terms: 0 + -9 = -9
-8n + n2 = -9

The n term is -8n.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8n + 16 + n2 = -9 + 16

Reorder the terms:
16 + -8n + n2 = -9 + 16

Combine like terms: -9 + 16 = 7
16 + -8n + n2 = 7

Factor a perfect square on the left side:
(n + -4)(n + -4) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(n + -4) equal to 2.645751311 and -2.645751311.

Subproblem 1

n + -4 = 2.645751311 Simplifying n + -4 = 2.645751311 Reorder the terms: -4 + n = 2.645751311 Solving -4 + n = 2.645751311 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + n = 2.645751311 + 4 Combine like terms: -4 + 4 = 0 0 + n = 2.645751311 + 4 n = 2.645751311 + 4 Combine like terms: 2.645751311 + 4 = 6.645751311 n = 6.645751311 Simplifying n = 6.645751311

Subproblem 2

n + -4 = -2.645751311 Simplifying n + -4 = -2.645751311 Reorder the terms: -4 + n = -2.645751311 Solving -4 + n = -2.645751311 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + n = -2.645751311 + 4 Combine like terms: -4 + 4 = 0 0 + n = -2.645751311 + 4 n = -2.645751311 + 4 Combine like terms: -2.645751311 + 4 = 1.354248689 n = 1.354248689 Simplifying n = 1.354248689

Solution

The solution to the problem is based on the solutions from the subproblems. n = {6.645751311, 1.354248689}

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