Complete the square to transform quadratics and derive the quadratic formula.
Find the term to add when completing the square in x^2 + (b/a)x
Problem
For \(x^{2}+(b/a)x=-c/a\), determine the term that completes the square on the left. Halve the \(x\)-coefficient, square it, and express the result with powers of \(a\) and \(b\).
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What this problem is really about
The completing term comes from the full fractional coefficient of x. We’ll divide that coefficient by two, square both its numerator and denominator, simplify the resulting fraction, and verify it by expanding the corresponding binomial square.
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