Song for the Square Root Method with an Additional Dimension

The Square Root Method with an Additional Dimension Pingfang dai zong fa: A method for extracting roots where the shape is a rectangle rather than a square; equivalent to solving the quadratic equation x² + ax = Area is truly marvelous,
First, place the longitudinal steps Zong: The linear coefficient or the difference between length and width as the base in the lower position.

Add the value of the upper quotient Shang: The digits of the root being calculated into the longitudinal value;
The longitudinal and the square in the lower method combine to form the divisor.

The upper and lower digits call out to each other to exhaust the dividend Shi: The area or total value from which the root is extracted.
When extracting the remainder, double the "square" part, but do not double the "longitudinal" part.

With the remaining sum, continue to find the quotient and double the square again;
Why worry that this technique cannot be understood?

The method says: Suppose there is a field with an area of a certain amount. It is only stated that the width is less than the length by a certain amount. To find the width: $\bigcirc$ Set the field area of a certain amount as the dividend (shi). Take the amount by which the width is less than the length as the longitudinal (zong) and list it in the lower method. Divide it using the "Square Root Method with an Additional Dimension."

On the dividend, the first quotient obtained is a certain amount. In the lower method, also place this first quotient into the longitudinal position to get a total of a certain amount. Multiply the upper quotient by this total and subtract the product from the dividend a certain amount, leaving a remainder of a certain amount.

Separately, take the first quotient in the lower method and double it doubled square, but do not double the longitudinal. $\bigcirc$ Place the second quotient a certain amount in the left position following the first quotient. In the lower method, also place the second quotient a certain amount next to the doubled square, making a total of a certain amount. Multiply the second quotient by this total to exhaust the dividend. This gives the value of the width. Add the "less than" amount the difference between length and width to find the length.