n^2=9n-8

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


Simplifying
n2 = 9n + -8

Reorder the terms:
n2 = -8 + 9n

Solving
n2 = -8 + 9n

Solving for variable 'n'.

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

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

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

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

Factor a trinomial.
(1 + -1n)(8 + -1n) = 0

Subproblem 1

Set the factor '(1 + -1n)' equal to zero and attempt to solve: Simplifying 1 + -1n = 0 Solving 1 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1n = 0 + -1 -1n = 0 + -1 Combine like terms: 0 + -1 = -1 -1n = -1 Divide each side by '-1'. n = 1 Simplifying n = 1

Subproblem 2

Set the factor '(8 + -1n)' equal to zero and attempt to solve: Simplifying 8 + -1n = 0 Solving 8 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1n = 0 + -8 -1n = 0 + -8 Combine like terms: 0 + -8 = -8 -1n = -8 Divide each side by '-1'. n = 8 Simplifying n = 8

Solution

n = {1, 8}

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