Question

solve by completing the square.
\\(y = x^2 + 4x - 7\\)
\\(7 + 4 = x^2 + 4x + 4\\)
\\(11 = (x + ?)^2\\)

what number belongs in the green box?
2
4

Explanation:

Identify the trinomial to factor

Using the Completing the Square knowledge point

$$ x^2 + 4x + 4 $$

Factor the perfect square trinomial

Using the Perfect Square Trinomials knowledge point

$$ x^2 + 2(2)x + 2^2 = (x + 2)^2 $$

Determine the missing value

Using the Completing the Square knowledge point

$$ 11 = (x + [?])^2 \implies [?] = 2 $$

Answer:

• 2 (Correct answer)
• 4