Answer
{$-4 - 2i\sqrt 2,-4 + 2i\sqrt 2$}
Work Step by Step
Step 1: Comparing $y^{2}+8y+24=0$ to the standard form of a quadratic equation, $ay^{2}+by+c=0$, we find:
$a=1$, $b=8$ and $c=24$
Step 2: The quadratic formula is:
$y=\frac{-b \pm \sqrt {b^{2}-4ac}}{2a}$
Step 3: Substituting the values of a, b and c in the formula:
$y=\frac{-(8) \pm \sqrt {(8)^{2}-4(1)(24)}}{2(1)}$
Step 4: $y=\frac{-8 \pm \sqrt {64-96}}{2}$
Step 5: $y=\frac{-8 \pm \sqrt {-32}}{2}$
Step 6: $y=\frac{-8 \pm \sqrt {-1\times32}}{2}$
Step 7: $y=\frac{-8 \pm (\sqrt {-1}\times\sqrt {32})}{2}$
Step 8: $y=\frac{-8 \pm (\sqrt {-1}\times\sqrt {16\times2})}{2}$
Step 9: $y=\frac{-8 \pm (i\times 4\sqrt 2)}{2}$
Step 10: $y=\frac{-8 \pm 4i\sqrt 2}{2}$
Step 11: $y=\frac{2(-4 \pm 2i\sqrt 2)}{2}$
Step 12: $y=-4 \pm 2i\sqrt 2$
Step 13: $y=-4 - 2i\sqrt 2$ or $y=-4 + 2i\sqrt 2$
Step 14: Therefore, the solution set is {$-4 - 2i\sqrt 2,-4 + 2i\sqrt 2$}.
