54000002997 × 3000 - 416793 = 162000008574207
Now try the value of the above when x = 30. We have then, for the steps, 60 (2 × 30 + 0), 1801, 54027, and lastly,
1620810 - 416793,
or x = 30 makes the first terms greater than 416793. Now try x = 20 which gives 40, 801, 16017, and lastly,
320340 - 416793,
or x = 20 makes the first terms less than 416793. Between 20 and 30, then, must be a value of x which makes 2x⁴ + x²-3x equal to 416793. And this is the preliminary step of the process.
Having got thus far, write down the coefficients +2, 0, +1,-3, and -416793, each with its proper algebraical sign, except the last, in which let the sign be changed. This is the most convenient way when the last sign is-. But if the last sign be +, it may be more convenient to let it stand, and change all which come before. Thus, in solving x³-12x + 1 = 0, we might write
-1 0 +12 1
whereas in the instance before us, we write
+2 0 +1 -3 416793