Complete the square to transform quadratics and derive the quadratic formula.
Complete the square for a quadratic of the form x^2 + bx + c
Problem
Rewrite \(x^{2}+8x+5\) in completed-square form. Use half the linear coefficient to build a perfect-square trinomial and compensate for the value introduced.
Big Picture
What this problem is really about
Completing the square means building a perfect-square trinomial without changing the expression’s value. We’ll take half the linear coefficient and square it, add and subtract that same amount, factor the three-term square, and combine the leftover constants.
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