## Algebra: A Combined Approach (4th Edition)

{$\frac{-1 + i\sqrt {35}}{6},\frac{-1 - i\sqrt {35}}{6}$}
$p=-3p^{2}-3$ can be rearranged as $3p^{2}+p+3=0$ Now solving $3p^{2}+p+3=0$: Step 1: Comparing $3p^{2}+p+3=0$ to the standard form of a quadratic equation $ax^{2}+bx+c=0$; $a=3$, $b=1$ and $c=3$ Step 2: The quadratic formula is: $x=\frac{-b \pm \sqrt {b^{2}-4ac}}{2a}$ Step 3: Substituting the values of a,b and c in the formula: $x=\frac{-(1) \pm \sqrt {1^{2}-4(3)(3)}}{2(3)}$ Step 4: $x=\frac{-1 \pm \sqrt {1-36}}{6}$ Step 5: $x=\frac{-1 \pm \sqrt {-35}}{6}$ Step 6: $x=\frac{-1 \pm \sqrt {-1\times35}}{6}$ Step 7: $x=\frac{-1 \pm \sqrt {-1}\times\sqrt {35}}{6}$ Step 8: $x=\frac{-1 \pm i\sqrt {35}}{6}$ Step 9: $x=\frac{-1 + i\sqrt {35}}{6}$ or $x=\frac{-1 - i\sqrt {35}}{6}$ Step 10: Therefore, the solution set is {$\frac{-1 + i\sqrt {35}}{6},\frac{-1 - i\sqrt {35}}{6}$}.