How do you factor 6k ^ { 2} = 34+ 5k?

2 Answers
Nov 4, 2017

k=17/6or k=-2

Explanation:

To solve this question, we can put all things to one side.

6k^2=34+5k

6k^2-5k-34=0

And we can use cross method to factorize the L.H.S. .

(6k-17)(k+2)=0

then, we get

6k-17=0 or k+2=0

k=17/6or k=-2

Here is the answer. Hope this can help you :)

Nov 4, 2017

(k + 2)(6k - 17)

Explanation:

Use the new AC Method to factor trinomials (Socratic Search).
f(k) = 6k^2 - 5k - 34 = 6(k + p)k + q)
Converted trinomial:
f'(k) = k^2 - 5k - 204 = (k + p')(k + q')
Proceed: find p' and q', then, divide them by a = 6 to get p and q.
Compose factor pairs of (ac = - 204) --> ...(6, - 34)(12, - 17). This last sum is -5. Therefor, p' = 12 and q' = - 17
Back to f(k), p = (p')/a = 12/6 = 2, and q = (q')/a = - 17/6
Factored form:
f(k) = 6(k + 2)(k - 17/6) = (k + 2)(6k - 17)