1 Answer

Aldo · Answer 1 · 2024-12-23T09:15:01+0000

Answer:

(x+2)^2-16

Explanation:

Given quadratic expression:

x^2+4x-12

To complete the square, add and subtract the square of half the coefficient of the term in x after the term in x:

$\implies x^2+4x+\left((4)/(2)\right)^2-\left((4)/(2)\right)^2-12$

Simplify:

$\implies x^2+4x+\left(2\right)^2-\left(2\right)^2-12$

$\implies x^2+4x+4-4-12$

The first three terms form a perfect square trinomial which can be factored:

$\implies \boxed{x^2+4x+4}-4-12$

$\implies \boxed{(x+2)^2}-4-12$

Finally, subtract the numbers:

$\implies (x+2)^2-16$

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