Complete the square to transform quadratics and derive the quadratic formula.
Solve a monic quadratic equation by completing the square
Problem
Solve \(x^{2}+6x+5=0\) by completing the square. Transform the equation into a squared-binomial equation, apply both square-root branches, and report the complete solution set.
Big Picture
What this problem is really about
Completing the square lets us replace the quadratic and linear terms with one squared binomial. We’ll move the constant, add the square of half the linear coefficient to both sides, factor the perfect square, and take both square-root branches so the complete solution set is retained.
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