Question

how do i solve for all real values of x in this one? thanks..
6 (x + 2)^4 - 11 (x + 2)^2 = -4

Answer 1

i would also change a nicer looking variable for that x+2

Answer 2

then, same as before, synthetic division, those 4 and 6 terms are shouting to be divided

Answer 3

let u = (x + 2)^2

then rewriting the equation gives

6u^2 - 11u + 4 = 0

solve the quadratic

(2u -1)(3u - 4) = 0

u = 1/2 and 4/3

then replacing u with (x + 2)^2

(x + 2)^2 = 1/2

solve for x

\[x + 2 = \pm \sqrt{1/2} \]

\[x = -2\pm \sqrt{1/2}\]

I'll let you solve the other solution of 4/3

Answer 4

thanks, dears! :)