Question

Maths, completing the square, please help! I don't know why my answer is wrong. Please explain how to do this question.

Answer 1

`(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`