Question

3. Which of the following equations is equivalent to the equation shown below? x^2 + 4x + 15 = 0

Answer 1

We need to expand the answer choices and see which one matches the equation

$x^2+4x+15=0$

Remember the algebraic rules:

$(a\pm b)^2=a^2\pm2ab+b^2$

Now, if we expand choice D, we should get this. Let's expand:

$\begin{gathered} (x+2)^2=-11 \\ x^2+2(1)(2)+(2)^2=-11 \\ x^2+4x+4=-11 \\ x^2+4x+4+11=0 \\ x^2+4x+15=0 \end{gathered}$