Part 2/4:
The essence of the PQ method lies in shifting the parabola defined by the quadratic equation. The goal of this shift is to eliminate the linear term ( px ), simplifying the expression further.
To achieve this, a new variable ( y ) is introduced through the substitution:
[ x = y + k ]
where ( k ) is a constant chosen to eliminate the ( px ) term. Upon substituting ( x ) with ( y + k ) in our equation, we engage in expanding the terms to reveal a new form of the quadratic equation.
Establishing the Value of K
Through the expansion process, we notice key terms that emerge:
[ (y + k)^2 + p(y + k) + q = 0 ]