Question

Please help

Complete the square.

x2+6x+15

A) (x+3)2+6
B) (x+3)2+12
C) (x+6)2−21
D) (x+6)2+9

Answer 1

I found this on an app I used it by completing the square but it didn't show this

Answer 2

The correct option is A because the expression after completing the square is $(x+3)^2+6$.

The given equation is:

• $x^2+6x+15$

Explanation:

To complete the square, add and subtract the square of half of the coefficient of $x$, i.e., $\left(\dfrac{6}{2}\right)^2=3^2$.

$x^2+6x+15=x^2+6x+15+3^2-3^2$

$x^2+6x+15=(x^2+2x(3)+3^2)+15-9$

$x^2+6x+15=(x+3)^2+6$                 $[\because (a+b)^2=a^2+2ab+b^2]$

Thus, the correct option is A.

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