9k^2-8k-1=0

Solution for 9k^2-8k-1=0 equation:

Simplifying
9k2 + -8k + -1 = 0

Reorder the terms:
-1 + -8k + 9k2 = 0

Solving
-1 + -8k + 9k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-1 + -9k)(1 + -1k) = 0

Subproblem 1
Set the factor '(-1 + -9k)' equal to zero and attempt to solve:

Simplifying
-1 + -9k = 0

Solving
-1 + -9k = 0

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

Add '1' to each side of the equation.
-1 + 1 + -9k = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -9k = 0 + 1
-9k = 0 + 1

Combine like terms: 0 + 1 = 1
-9k = 1

Divide each side by '-9'.
k = -0.1111111111

Simplifying
k = -0.1111111111
Subproblem 2
Set the factor '(1 + -1k)' equal to zero and attempt to solve:

Simplifying
1 + -1k = 0

Solving
1 + -1k = 0

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

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

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

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

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

Simplifying
k = 1
Solution
k = {-0.1111111111, 1}