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4''x''<sup>2</sup> – 16''x'' + 15 = 0
4''x''<sup>2</sup> – 16''x'' + 16 = 1
(2''x'' – 4)<sup>2</sup> = 1
2''x'' – 4 = ±1
2''x'' = 4 ± 1
''x'' = {{sfrac|4 ± 1|2}}
''x'' = {{sfrac|5|2}} and ''x'' = {{sfrac|3|2}}
Quadratic equation solved by square completion in late June or early summer 2022 by Shadow (37 by age at that time)
15''x''<sup>2</sup> – 16''x'' + 4 = 0
225''x''<sup>2</sup> – 240''x'' + 60 = 0
225''x''<sup>2</sup> – 240''x'' + 64 = 4
(15''x'' – 8)<sup>2</sup> = 4
15''x'' – 8 = ±2
15''x'' = 8 ± 2
''x'' = {{sfrac|8 ± 2|15}}
''x'' = {{sfrac|2|3}} and ''x'' = {{sfrac|2|5}}
Quadratic equation solved by square completion in late June or early summer 2022 by Silver (35 by age at that time)
6''x''<sup>2</sup> – 19''x'' + 15 = 0
144''x''<sup>2</sup> – 456''x'' + 360 = 0
144''x''<sup>2</sup> – 456''x'' + 361 = 1
(12''x'' – 19)<sup>2</sup> = 1
12''x'' – 19 = ±1
12''x'' = 19 ± 1
''x'' = {{sfrac|19 ± 1|12}}
''x'' = {{sfrac|5|3}} and ''x'' = {{sfrac|3|2}}
Quadratic equation solved by square completion in late June or early summer 2022 by Mighty (37 by age at that time)
15''x''<sup>2</sup> – 19''x'' + 6 = 0
900''x''<sup>2</sup> – 1,140''x'' + 360 = 0
900''x''<sup>2</sup> – 1,140''x'' + 361 = 1
(30''x'' – 19)<sup>2</sup> = 1
30''x'' – 19 = ±1
30''x'' = 19 ± 1
''x'' = {{sfrac|19 ± 1|30}}
''x'' = {{sfrac|2|3}} and ''x'' = {{sfrac|3|5}}
Quadratic equation solved by square completion in late June or early summer 2022 by Sonic (36 by age at that time)
6''x''<sup>2</sup> – 25''x'' + 25 = 0
144''x''<sup>2</sup> – 600''x'' + 600 = 0
144''x''<sup>2</sup> – 600''x'' + 625 = 25
(12''x'' – 25)<sup>2</sup> = 25
12''x'' – 25 = ±5
12''x'' = 25 ± 5
''x'' = {{sfrac|25 ± 5|12}}
''x'' = {{sfrac|5|2}} and ''x'' = {{sfrac|5|3}}
Quadratic equation solved by square completion in late June or early summer 2022 by Ray (30 by age at that time)
25''x''<sup>2</sup> – 25''x'' + 6 = 0
100''x''<sup>2</sup> – 100''x'' + 24 = 0
100''x''<sup>2</sup> – 100''x'' + 25 = 1
(10''x'' – 5)<sup>2</sup> = 1
10''x'' – 5 = ±1
10''x'' = 5 ± 1
''x'' = {{sfrac|5 ± 1|10}}
''x'' = {{sfrac|3|5}} and ''x'' = {{sfrac|2|5}}
Quadratic equation solved by square completion in late June or early summer 2022 by Tails (29 by age at that time)
6''x''<sup>2</sup> – 19''x'' + 10 = 0
144''x''<sup>2</sup> – 456''x'' + 240 = 0
144''x''<sup>2</sup> – 456''x'' + 361 = 121
(12''x'' – 19)<sup>2</sup> = 121
12''x'' – 19 = ±11
12''x'' = 19 ± 11
''x'' = {{sfrac|19 ± 11|12}}
''x'' = {{sfrac|5|2}} and ''x'' = {{sfrac|2|3}}
Quadratic equation solved by square completion in late June or early summer 2022 by Mina (37 by age at that time)
10''x''<sup>2</sup> – 19''x'' + 6 = 0
400''x''<sup>2</sup> – 760''x'' + 240 = 0
400''x''<sup>2</sup> – 760''x'' + 361 = 121
(20''x'' – 19)<sup>2</sup> = 121
20''x'' – 19 = ±11
20''x'' = 19 ± 11
''x'' = {{sfrac|19 ± 11|20}}
''x'' = {{sfrac|3|2}} and ''x'' = {{sfrac|2|5}}
Quadratic equation solved by square completion in late June or early summer 2022 by Tikal (35 by age at that time)
9''x''<sup>2</sup> – 21''x'' + 10 = 0
36''x''<sup>2</sup> – 84''x'' + 40 = 0
36''x''<sup>2</sup> – 84''x'' + 49 = 9
(6''x'' – 7)<sup>2</sup> = 9
6''x'' – 7 = ±3
6''x'' = 7 ± 3
''x'' = {{sfrac|7 ± 3|6}}
''x'' = {{sfrac|5|3}} and ''x'' = {{sfrac|2|3}}
Quadratic equation solved by square completion in late June or early summer 2022 by Rouge (38 by age at that time)
10''x''<sup>2</sup> – 21''x'' + 9 = 0
400''x''<sup>2</sup> – 840''x'' + 360 = 0
400''x''<sup>2</sup> – 840''x'' + 441 = 81
(20''x'' – 21)<sup>2</sup> = 81
20''x'' – 21 = ±9
20''x'' = 21 ± 9
''x'' = {{sfrac|21 ± 9|20}}
''x'' = {{sfrac|3|2}} and ''x'' = {{sfrac|3|5}}
Quadratic equation solved by square completion in late June or early summer 2022 by Blaze (35 by age at that time)
10''x''<sup>2</sup> – 31''x'' + 15 = 0
400''x''<sup>2</sup> – 1,240''x'' + 600 = 0
400''x''<sup>2</sup> – 1,240''x'' + 961 = 361
(20''x'' – 31)<sup>2</sup> = 361
20''x'' – 31 = ±19
20''x'' = 31 ± 19
''x'' = {{sfrac|31 ± 19|20}}
''x'' = {{sfrac|5|2}} and ''x'' = {{sfrac|3|5}}
Quadratic equation solved by square completion in late June or early summer 2022 by Sally (36 by age at that time)
15''x''<sup>2</sup> – 31''x'' + 10 = 0
900''x''<sup>2</sup> – 1,860''x'' + 600 = 0
900''x''<sup>2</sup> – 1,860''x'' + 961 = 361
(30''x'' – 31)<sup>2</sup> = 361
30''x'' – 31 = ±19
30''x'' = 31 ± 19
''x'' = {{sfrac|31 ± 19|30}}
''x'' = {{sfrac|5|3}} and ''x'' = {{sfrac|2|5}}
Quadratic equation solved by square completion in late June or early summer 2022 by Marine (28 by age at that time)
6''x''<sup>2</sup> – 13''x'' + 6 = 0
144''x''<sup>2</sup> – 312''x'' + 144 = 0
144''x''<sup>2</sup> – 312''x'' + 169 = 25
(12''x'' – 13)<sup>2</sup> = 25
12''x'' – 13 = ±5
12''x'' = 13 ± 5
''x'' = {{sfrac|13 ± 5|12}}
''x'' = {{sfrac|3|2}} and ''x'' = {{sfrac|2|3}}
Quadratic equation solved by square completion in late June or early summer 2022 by Amy (32 by age at that time)
10''x''<sup>2</sup> – 29''x'' + 10 = 0
400''x''<sup>2</sup> – 1,160''x'' + 400 = 0
400''x''<sup>2</sup> – 1,160''x'' + 841 = 441
(20''x'' – 29)<sup>2</sup> = 441
20''x'' – 29 = ±21
20''x'' = 29 ± 21
''x'' = {{sfrac|29 ± 21|20}}
''x'' = {{sfrac|5|2}} and ''x'' = {{sfrac|2|5}}
Quadratic equation solved by square completion in late June or early summer 2022 by Tangle (35 by age at that time)
15''x''<sup>2</sup> – 34''x'' + 15 = 0
225''x''<sup>2</sup> – 510''x'' + 225 = 0
225''x''<sup>2</sup> – 510''x'' + 289 = 64
(15''x'' – 17)<sup>2</sup> = 64
15''x'' – 17 = ±8
15''x'' = 17 ± 8
''x'' = {{sfrac|17 ± 8|15}}
''x'' = {{sfrac|5|3}} and ''x'' = {{sfrac|3|5}}
Quadratic equation solved by square completion in late June or early summer 2022 by Knuckles (36 by age at that time)
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