10k^2+9k=1

Solution for 10k^2+9k=1 equation:

Simplifying
10k2 + 9k = 1

Reorder the terms:
9k + 10k2 = 1

Solving
9k + 10k2 = 1

Solving for variable 'k'.

Reorder the terms:
-1 + 9k + 10k2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 9k + 10k2 = 0

Factor a trinomial.
(-1 + -1k)(1 + -10k) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(1 + -10k)' equal to zero and attempt to solve:

Simplifying
1 + -10k = 0

Solving
1 + -10k = 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 + -10k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -10k = 0 + -1
-10k = 0 + -1

Combine like terms: 0 + -1 = -1
-10k = -1

Divide each side by '-10'.
k = 0.1

Simplifying
k = 0.1
Solution
k = {-1, 0.1}