## Two Solutions by Quinapalus

### Puzzle explanation

The corrections to clue misprints spelt out “indices, surds; move both Xs vertically”. The grid entries containing two words gave Rev. C. L. Dodgson, his nom de plume Lewis Carroll, and the (abbreviated) titles of two of his books, Rhyme? And Reason? and Phantasmagoria (and Other Poems). A verse cited in both books includes:

Yet what are all such gaieties to me
Whose thoughts are full of indices and surds?
x2 + 7x + 53
= 11/3.

The quadratic equation has two complex solutions, (−7 ± √(−445/3))/2, which are approximately x = −3.5 ± 6.0896i. Nudging the two Xs in the grid to a distance of more or less 6.1 cells above and below the central axis, encroaching on the previously empty cells to form new words reading across, marks the two complex numbers as in an Argand diagram.

For the cells containing two letters, it didn’t matter which (opposite) corners they were placed into, as long as the letters of each of the two entries, as well as ARGAND DIAGRAM, could be read normally, as stated in the preamble.

### Clue explanations

Conventions: * = anagram, < = reversal

Across
1 F(I)x SET 2 meanings
4   PARA, PAPA PA around A
7 (N)ellie BERK KERB *
11 (D)Js TUXES TIES with UX for I
13 l(I)ver THIAMIN (I + HITMAN) *
15 La(C)una ARMPIT A + (M + TRIP) *
16 c(E)ll LYSIS homophone of LY + SIS
17   SNUGGLE, SMUGGLE GUS < + LEG *
18 Bour(S)e EASDAQ EQ around ASDA
22 (S)ea AQUA A + QU + A
23 R(U)ss ONEGA GONE with letters “cycling” + A
25   REINVEST, REINVENT REIN + VET
26 Ai(R)ed DJED DATED with J for AT
27   TRANSUME, TRANSUDE (TEA URNS) *
29 (D)educed DREW DR DRE − DR + W
32   ODER, ODEA ODE
33 Stock(S) CIPPI ’IPPIC <
35 Cre(M)e CASSIS CHASSIS − H(ose)
38   LEWIS, REV C L
41   CARROLL, DODGSON
43 (O)ver ITERUM GRUMPIEST * − GPS *
44 li(V)ing MIXEN MIX + EN
45   FIRMERS, FORMERS F(ea)R(so)M(e r)E(se)R(vi)S(t)
46 w(E)ll SAE ’S + A + E(legance)
47   GENT, GEAT GET
48 (B)ounty PRYS PRY’S
Down
1 m(O)re STALER STA(b)LER
2 s(T)are EURYALE RUE * + YALE
3 Warmis(H) TEPID P in TIDE *
4 (X)s PSIS PS + IS
5   PHANTASMAGORIA, RHYME AND REASON
6 i(S)landers AITU IT in AU
8 lea(V)er ÉMIGRÉ (ÉMIGRÉ + HAT) * = HERMITAGE
9 l(E)af RIZLA (c)RAZIL(y) *
10 buckle(R) KNEE-PAD (DAK around (PEE + ’N’)) <
12 s(T)ore XMS XMAS − A
14   ARGAND DIAGRAM
19 Al(I) SHIAHS SHAHS around I
20 Lo(C)ks QUEUES 2 meanings
21 p(A)st NO-TECH E in NOTCH