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Completing the square is an algebraic technique that converts a quadratic expression into perfect square form. It's used to solve quadratics and rewrite parabola equations in vertex form.

Formula

ax² + bx + c = a(x + b/2a)² + (c - b²/4a)

Guida passo passo

1Identify coefficients a, b, c
2Move constant to the right side
3Add (b/2a)² to both sides to complete the square

Esempi risolti

Ingresso

x² + 6x + 5 = 0

Risultato

(x + 3)² = 4 → x = -1 or x = -5

Completing the square yields vertex form

Errori comuni da evitare

✕Forgetting the a coefficient when factoring out
✕Adding wrong value to complete the square

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