50k^2-60k+19=1

Solution for 50k^2-60k+19=1 equation:

Simplifying
50k2 + -60k + 19 = 1

Reorder the terms:
19 + -60k + 50k2 = 1

Solving
19 + -60k + 50k2 = 1

Solving for variable 'k'.

Reorder the terms:
19 + -1 + -60k + 50k2 = 1 + -1

Combine like terms: 19 + -1 = 18
18 + -60k + 50k2 = 1 + -1

Combine like terms: 1 + -1 = 0
18 + -60k + 50k2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + -30k + 25k2) = 0

Factor a trinomial.
2((3 + -5k)(3 + -5k)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -5k)' equal to zero and attempt to solve:

Simplifying
3 + -5k = 0

Solving
3 + -5k = 0

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

Add '-3' to each side of the equation.
3 + -3 + -5k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5k = 0 + -3
-5k = 0 + -3

Combine like terms: 0 + -3 = -3
-5k = -3

Divide each side by '-5'.
k = 0.6

Simplifying
k = 0.6
Subproblem 2
Set the factor '(3 + -5k)' equal to zero and attempt to solve:

Simplifying
3 + -5k = 0

Solving
3 + -5k = 0

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

Add '-3' to each side of the equation.
3 + -3 + -5k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5k = 0 + -3
-5k = 0 + -3

Combine like terms: 0 + -3 = -3
-5k = -3

Divide each side by '-5'.
k = 0.6

Simplifying
k = 0.6
Solution
k = {0.6, 0.6}