Question

10. (09.02 MC)Which of the following tables shows the correct steps to transform x2 + 8x + 15 = 0 into the form (x - p)2 = q?[p and q are integers) (5 points)

Answer 1

To transform

$x^2+8x+15=0$

Make it a perfect square

since 8x/2 = 4x, then

We need to make 15 = 16 for 4 x 4 = 16, so add 1 and subtract 1

$\begin{gathered} x^2+8x+(15+1)-1=0 \\ x^2+8x+16-1=0 \end{gathered}$

Now we will make the bracket to the power of 2

$\begin{gathered} (x^2+8x+16)-1=0 \\ (x+4)^2-1=0 \end{gathered}$

Add 1 to both sides

$\begin{gathered} (x+4)^2-1+1=0+1 \\ (x+4)^2=1 \end{gathered}$

The answer is C