13) v^2-3v-154= 15) n^2-n-132= 17) r^2+10r-171= 19) x^2+27x+182= 21) 5x^2+55x+140= 23) 3p^2-30p+48= 14) x^2-26x+165= 16) x^2-21x+104= 18) x^2-10x-200= 20) x^2+29x+204= 22) 5x^3+10x^2-315x= 24) 6x^2-66x+108=

13) $$v^{2}-3v-154=0$$
To solve this quadratic equation, we can use the quadratic formula:
$$v=\frac{-(-3) \pm \sqrt{(-3)^{2}-4(1)(-154)}}{2(1)}$$
$$v=\frac{3 \pm \sqrt{9+616}}{2}$$
$$v=\frac{3 \pm \sqrt{625}}{2}$$
$$v=\frac{3 \pm 25}{2}$$
Therefore, the solutions are $$v=14$$ and $$v=-11$$ .

15) $$n^{2}-n-132=0$$
Using the quadratic formula:
$$n=\frac{-(-1) \pm \sqrt{(-1)^{2}-4(1)(-132)}}{2(1)}$$
$$n=\frac{1 \pm \sqrt{1+528}}{2}$$
$$n=\frac{1 \pm \sqrt{529}}{2}$$
$$n=\frac{1 \pm 23}{2}$$
Therefore, the solutions are $$n=12$$ and $$n=-11$$ .

17) $$r^{2}+10r-171=0$$
Using the quadratic formula:
$$r=\frac{-(10) \pm \sqrt{(10)^{2}-4(1)(-171)}}{2(1)}$$
$$r=\frac{-10 \pm \sqrt{100+684}}{2}$$
$$r=\frac{-10 \pm \sqrt{784}}{2}$$
$$r=\frac{-10 \pm 28}{2}$$
Therefore, the solutions are $$r=9$$ and $$r=-19$$ .

19) $$x^{2}+27x+182=0$$
Using the quadratic formula:
$$x=\frac{-(27) \pm \sqrt{(27)^{2}-4(1)(182)}}{2(1)}$$
$$x=\frac{-27 \pm \sqrt{729-728}}{2}$$
$$x=\frac{-27 \pm \sqrt{1}}{2}$$
$$x=\frac{-27 \pm 1}{2}$$
Therefore, the solutions are $$x=-13$$ and $$x=-14$$ .

21) $$5x^{2}+55x+140=0$$
Using the quadratic formula:
$$x=\frac{-(55) \pm \sqrt{(55)^{2}-4(5)(140)}}{2(5)}$$
$$x=\frac{-55 \pm \sqrt{3025-2800}}{10}$$
$$x=\frac{-55 \pm \sqrt{225}}{10}$$
$$x=\frac{-55 \pm 15}{10}$$
Therefore, the solutions are $$x=-7$$ and $$x=-4$$ .

23) $$3p^{2}-30p+48=0$$
Using the quadratic formula:
$$p=\frac{-(30) \pm \sqrt{(30)^{2}-4(3)(48)}}{2(3)}$$
$$p=\frac{-30 \pm \sqrt{900-576}}{6}$$
$$p=\frac{-30 \pm \sqrt{324}}{6}$$
$$p=\frac{-30 \pm 18}{6}$$
Therefore, the solutions are $$p=4$$ and $$p=4$$ .

14) $$x^{2}-26x+165=0$$
Using the quadratic formula:
$$x=\frac{-(26) \pm \sqrt{(26)^{2}-4(1)(165)}}{2(1)}$$
$$x=\frac{-26 \pm \sqrt{676-660}}{2}$$
$$x=\frac{-26 \pm \sqrt{16}}{2}$$
$$x=\frac{-26 \pm 4}{2}$$
Therefore, the solutions are $$x=15$$ and $$x=11$$ .

16) $$x^{2}-21x+104=0$$
Using the quadratic formula:
$$x=\frac{-(21) \pm \sqrt{(21)^{2}-4(1)(104)}}{2(1)}$$
$$x=\frac{-21 \pm \sqrt{441-416}}{2}$$
$$x=\frac{-21 \pm \sqrt{25}}{2}$$
$$x=\frac{-21 \pm 5}{2}$$
Therefore, the solutions are $$x=16$$ and $$x=5$$ .

18) $$x^{2}-10x-200=0$$
Using the quadratic formula:
$$x=\frac{-(10) \pm \sqrt{(10)^{2}-4(1)(-200)}}{2(1)}$$
$$x=\frac{-10 \pm \sqrt{100+800}}{2}$$
$$x=\frac{-10 \pm \sqrt{900}}{2}$$
$$x=\frac{-10 \pm 30}{2}$$
Therefore, the solutions are $$x=20$$ and $x