Complete the square to transform quadratics and derive the quadratic formula.
Find the value to add to \(x^2 + bx\) to complete the square
Problem
What value must be added to \(x^2+12x\) to complete the square?
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What this problem is really about
For a monic expression, the completing value is not the linear coefficient itself or its square. We’ll halve the coefficient first, square the result, and confirm that adding this value creates a trinomial whose middle term is twice x times the binomial’s constant.
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