History of Hindu Mathematics: A Source Book v2.c17.s17.t5.24

v2.c17.s17.t5.24

Multiplying both sides of the equation (5) by *a* and then completing a square on the left-hand side, the equation transforms into $(ax + ½by)² + (ac - ¼b²)y² = az².$ Putting ax + ½by = w and β = ¼(b² - 4ac), we get w² = az² + β y². (5.3)