I cannot figure out how to do this
Solve for k
-1/3 is a solution
Solve for k:
k x^2-13 x = 5
Add 13 x to both sides:
k x^2 = 13 x+5
Divide both sides by x^2:
Answer: | k = 13/x+5/x^2
P.S. You cannot get a numerical value for k, because you have 2 unknowns, x and k. You can only solve for k in terms of x.
+33653 k*x^2 -13*x - 5 = 0
Use the quadratic formula to obtain solutions: x1 = (13 - sqrt(20*k + 169))/(2k) and x2 = (13 + sqrt(20*k + 169))/(2k)
Only x1 could be -1/3, so:
(13 - sqrt(20*k + 169))/(2k) = -1/3
3*(13 - sqrt(20*k + 169)) = -2k
39 = 3*sqrt(20k + 169) - 2k
39 + 2k = 3*sqrt(20k + 169)
Square both sides:
39^2 + 4*39*k + 4k^2 = 9*(20k + 169)
4k^2 - 24k = 0
k(k - 6) = 0
k = 0 or k = 6 (Only the k = 6 solution keeps the original equation as a quadratic).
