Complete the square to transform quadratics and derive the quadratic formula.
Add the completing-square term when deriving the quadratic formula
Problem
In a derivation of the quadratic formula from \(ax^2+bx+c=0\), what is the next algebra step after \(x^2+(b/a)x=-c/a\)?
Big Picture
What this problem is really about
At this point in the quadratic-formula derivation, the left side is monic and its full linear coefficient is the fraction b over a. We’ll halve that entire fraction, square it, and add the same term to both sides so the next line is balanced and the left side becomes a perfect-square trinomial.
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