1 0 -10 -1(3·1110390520730990796 3 -1 2000 6 1700 209000 9 0 1791 19769000 9 1 188300 743369000000 9 2 189231 172311710273000 9 30 19016300 991247447681 9 31 19025631 39462875420 9 32 1903496300 0 0 1391491559 9 33 0 1903524299 0 9 58993123 9 33 1 1903552298 2 7 0 0 1886047 9 33 2 1903560698 0 5|9|1 172835 9 33 30 0 1903569097 8 5|6|3 1515 9 33 30 3 1903569144 5 2|2| 183 9 33 30 6 1903569191 1|8|8 12 9 33 30 90 1903569193 0|6| 1 9 33|30|99 1903569194|9|3| 9 33|31|08 | | | |09|33|31|17 | | | | The student need not repeat the rows of figures so far as they come under one another: thus, it is not necessary to repeat 190356. But he must use his own discretion as to how much it would be safe for him to omit. I have set down the whole process here as a guide. The following examples will serve for exercise: 1. 2_x_³ - 100_x_ - 7 = 0 _x_ = 7·10581133. 2. _x_⁴ + _x_³ + _x_² + _x_ = 6000 _x_ = 8·531437726. 3. _x_³ + 3_x_² - 4_x_ - 10 = 0 _x_ = 1·895694916504. 4. _x_³ + 100_x_² - 5_x_ - 2173 = 0 _x_ = 4·582246071058464. _ 5. ∛2 = 1·259921049894873164767210607278.[69] 6. _x_³ - 6_x_ = 100 _x_ = 5·071351748731. 7. _x_³ + 2_x_² + 3_x_ = 300 _x_ = 5·95525967122398. 8. _x_³ + _x_ = 1000 _x_ = 9·96666679. 9. 27000_x_³ + 27000_x_ = 26999999 _x_ = 9·9666666..... 10. _x_³ - 6_x_ = 100 _x_ = 5·0713517487. 11. _x_⁵ - 4_x_⁴ + 7_x_³ - 863 = 0 _x_ = 4·5195507. 12. _x_³ - 20_x_ + 8 = 0 _x_ = 4·66003769300087278. 13. _x_³ + _x_² + _x_ - 10 = 0 _x_ = 1·737370233. 14. _x_³ - 46_x_² - 36_x_ + 18 = 0 _x_ = 46·7616301847, or _x_ = ·3471623192. 15. _x_³ + 46_x_² - 36_x_ - 18 = 0 _x_ = 1·1087925037. 16. 8991_x_³ - 162838_x_² + 746271_x_ - 81000 = 0 _x_ = ·111222333444555.... 17. 729_x_³ - 486_x_² + 99_x_ - 6 = 0 _x_ = ·1111..., or ·2222..., or ·3333.... 18. 2_x_³ + 3_x_² - 4_x_ = 500 _x_ = 5·93481796231515279. 19. _x_³ + 2_x_² + _x_ - 150 = 0 _x_ = 4·6684090145541983253742991201705899. 20. _x_³ + _x_ = _x_² + 500 _x_ = 8·240963558144858526963. 21. _x_³ + 2_x_² + 3_x_ - 10000 = 0 _x_ = 20·852905526009. 22. _x_⁵ - 4_x_ - 2000 = 0 _x_ = 4·581400362. 23. 10_x_³ - 33_x_² - 11_x_ - 100 = 0 _x_ = 4·146797808584278785. 24. _x_⁴ + _x_³ + _x_² + _x_ = 127694 _x_ = 18·64482373095.