Complete the square to transform quadratics and derive the quadratic formula.
Complete the square exactly for a monic quadratic with a fractional x-coefficient
Problem
Rewrite \(x^{2}+(1/2)x+3\) in exact completed-square form. Halve the fractional coefficient, square it, and express the adjusted constant with a common denominator.
Big Picture
What this problem is really about
Fractional coefficients use the same completing-square idea, but every value must stay exact. We’ll halve the fractional x coefficient, square that fraction, add and subtract the result, factor the perfect square, and combine the leftover constants using a common denominator.
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