Question 472716
Let u = x - 102. Our equation becomes (u+3)(u+1)(u-1)(u-3) = -16. We can rewrite this as


*[tex \LARGE (u^2 - 9)(u^2 - 1) = -16] (collect 1st, 4th terms and 2nd, 3rd terms)


*[tex \LARGE u^4 - 10u^2 + 9 = -16]


*[tex \LARGE u^4 - 10u^2 + 25 = 0]


*[tex \LARGE (u^2 - 5)(u^2 - 5) = 0]


*[tex \LARGE u = \pm \sqrt{5}]


Since this is equal to x-102, we have


*[tex \LARGE x - 102 = \pm \sqrt{5}]


*[tex \LARGE x = 102 \pm \sqrt{5}]