 By 1300, the Chinese had developed the counting board method to solving polynomial equations of any degree to any desired accuracy. To do this, each coefficient is set down on its own row on the counting board, and multiple passes are required. So to solve this cubic, first we'll set down the coefficients, the number on the top row, the sides, 18, the x coefficient on the next row, the squares, 13, the x squared coefficient, and then the cubes, 1, the x cubed coefficient. And we'll shift. The sides move one place, the squares move two places, and the cubes move three places. And as with the square root procedure, we shift until we go past the leading digit of the number. And so we'll guess a digit. As with the square root procedure, the guess is the largest value that allows the first pass to work. So let's guess 3. And we'll conduct our first pass. The guess 3 times cubes, 1, and add to squares. Then guess 3 times squares, 43, and add to sides. Guess 3 times sides, 1308, and now subtract from the number. And at this point we have to make multiple passes, and the important idea here is that each pass stops one place earlier than the preceding pass. So our first pass went all the way up to the number, so our second pass will have guess times cubes, and add to squares. Then guess times squares, and add to sides. And since our next product would take us up to the number, we stop. But we will take a third pass, our guess times cubes, and add to squares, and stop. And now we'll shift our numbers. Our sides move one place, squares move two, and cubes move three places. And we'll guess the next agent. We guess 4, and we make the first pass. Guess times cubes, and add to squares. Guess times squares, and add to sides. Guess times sides, and subtract from our number. And again we'll make additional passes with each pass stopping one place short of the previous one. So our second pass, guess times cubes, and add to squares. Guess times squares, and add to sides, and stop. Then our third pass, guess times cubes, and add to squares, and stop. And shift. Sides move one place, squares move two places, cubes move three places. And note that we've shifted past the original unit's place, so the next digit will be the first digit after the decimal point. And we guess 3. And we go through our first pass, guess times cubes, and add to squares. Guess times squares, and add to sides. Guess times sides, and subtract from the number. Our second pass, guess times cubes, and add to squares. Then guess times squares, and add to sides, and stop. And our third pass, guess times cubes, and add to squares, and stop. And shift. Sides move one place, squares move two places, cubes move three places. And we can lather, rinse, repeat to find additional digits of the root.