Complete the square to transform quadratics and derive the quadratic formula.
Transform a monic quadratic equation into a perfect-square equation by completing the square
Problem
Transform \(x^{2}+6x=7\) into an equivalent perfect-square equation. Add the square of half the \(x\)-coefficient to both sides and factor the left side.
Big Picture
What this problem is really about
The goal is to turn the quadratic side into one perfect-square binomial while keeping the equation equivalent. We’ll find the square of half the linear coefficient, add that same amount to both sides, factor the left side, and verify the transformation by expanding and reversing the balancing step.
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