k^2-3k-1=9

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Solution for k^2-3k-1=9 equation: 


Simplifying
k2 + -3k + -1 = 9

Reorder the terms:
-1 + -3k + k2 = 9

Solving
-1 + -3k + k2 = 9

Solving for variable 'k'.

Reorder the terms:
-1 + -9 + -3k + k2 = 9 + -9

Combine like terms: -1 + -9 = -10
-10 + -3k + k2 = 9 + -9

Combine like terms: 9 + -9 = 0
-10 + -3k + k2 = 0

Factor a trinomial.
(-2 + -1k)(5 + -1k) = 0


Subproblem 1
Set the factor '(-2 + -1k)' equal to zero and attempt to solve:

Simplifying
-2 + -1k = 0

Solving
-2 + -1k = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1k = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1k = 0 + 2
-1k = 0 + 2

Combine like terms: 0 + 2 = 2
-1k = 2

Divide each side by '-1'.
k = -2

Simplifying
k = -2

Subproblem 2
Set the factor '(5 + -1k)' equal to zero and attempt to solve:

Simplifying
5 + -1k = 0

Solving
5 + -1k = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1k = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1k = 0 + -5
-1k = 0 + -5

Combine like terms: 0 + -5 = -5
-1k = -5

Divide each side by '-1'.
k = 5

Simplifying
k = 5
Solution
k = {-2, 5}

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