Question

The solution set for 4x^2-11x=10?
Fractional form.

Answer 1

I got \[11+\sqrt{287}/8 , 11-\sqrt{287}/8\]

Answer 2

4x^2-11x=10 ; divide out the 4

x^2 - (11/4)x = 10/4 ; "complete the square", which is just
half of (11/4), and ^2 it

x^2 - (11/4)x + (11/8)^2 = 10/4 + (11/8)^2; clean it up

(x - 11/8)^2 = 10/4 + 121/64

(x - 11/8)^2 = 10(16)/4(16) + 121/64

(x - 11/8)^2 = (160+121)/64

(x - 11/8)^2 = 281/64 ; now sqrt the sides

x - (11/8) = +- sqrt(281)/8 ; and +11/8

x = (11/8) +- sqrt(281)/8 ; simplfy as wanted

Answer 3

and of course dbl chk me math ;)