Complete the square to transform quadratics and derive the quadratic formula.
Complete the square for a quadratic when the leading coefficient is not 1
Problem
Rewrite \(2x^{2}+8x+1\) in completed-square form. Factor \(2\) from the variable terms, complete the square inside the grouping, and account for the outside multiplier.
Big Picture
What this problem is really about
Because the leading coefficient is not one, we first factor it from both variable terms before completing the square inside the grouping. We’ll halve the new linear coefficient, add its square inside, and compensate for the full change created by the outside factor before combining constants.
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