35.)Add 1 to both sides\\\\$x^2+2x+1=3+1$\\\\Express the left side as a perfect square\\\\$(x+1)^2=4$\\\\Take the square-root of both sides\\\\$x+1=\pm 2$\\\\$x=-1\pm2$\\\\$x=3$ or $x=-5$\\\\Therefore, the solution set is\\\\$\left\{ -3,1 \right\}$36.)Transpose -2 to the other side and add 16 to both sides\\\\$y^2+8y+16=2+16$\\\\Express the left side as a perfect square\\\\$(y+4)^2=18$\\\\Take the square-root of both sides\\\\$(y+4)=\pm 3\sqrt{2}$\\\\$y=-4\pm 3\sqrt{2}$\\\\Therefore, the solution set is\\\\$\left\{ --4+3\sqrt{2}, -4-3\sqrt{2} \right\}$37.)Add 9 to both sides\\\\$t^2-6t+9=-5+9$\\\\Express the left-side as a perfect square\\\\$(t-3)^2=4$\\\\Take the square-root of both sides\\\\$t-3=\pm 2$\\\\$t=3\pm2$\\\\Therefore the solution set is\\\\$\left\{ 1,5 \right\}$38.)Add 25 to both sides\\\\$x^2+10x+25=-21+25$\\\\Express the left side as a perfect square\\\\$(x+5)^2=4$\\\\Take the square-root of both sides\\\\$x+5=\pm2$\\\\$x=-5\pm2$Therefore, the solution set is\\\\$\left\{ -7,-3 \right\}$39.) Transpose 3 to the other side and add 4 to both sides\\\\$y^2-4y+4=-3+4$\\\\Express the left side as a perfect square\\\\$(y-2)^2=1$\\\\Take the square-root of both sides\\\\

$y-2=\pm 1$\\\\$y=2\pm1$Therefore, the solution set is\\\\$\left\{ 1,3 \right\}$40.)Add $(7/2)^2=\dfrac{49}{4}$ to both sides\\\\$x^2-7x+\dfrac{49}{4}=-12+\dfrac{49}{4}$\\\\Express the left side as a perfect square\\\\$\left(x-\dfrac{7}{2}\right)^2=\dfrac{1}{4}$\\\\Take the square-root of both sides\\\\$x-\dfrac{7}{2}=\pm \dfrac{1}{2}$\\\\$x=\dfrac{7}{2}\pm \dfrac{1}{2}$\\\\Therefore, the solution set is\\\\$\left\{ 3,4 \right\}$41.)On the left side, factor out 2\\\\$2(p^2+4p)=-3$\\\\Add 8 to both sides\\\\$2(p^2+4p+4)=-3+8$\\\\Express the left side as a perfect square\\\\$2(p+2)^2=5$\\\\$(p+2)^2=\dfrac{5}{2}$\\\\Take the square-root of both sides.\\\\$p+2=\pm \sqrt{\dfrac{5}{2}}$\\\\$p=-2\pm \sqrt{\dfrac{5}{2}}$\\\\Simplify further,Therefore, the solution set is\\\\$\left\{ -2-\dfrac{\sqrt{10}}{2}, -2+\dfrac{\sqrt{10}}{2} \right\}$42.)Transpose 3 to the other side and factor out 2\\\\$2(x^2 -2x)=-3$\\\\Add 2 to both sides\\\\$2(x^2-2x+1)=-3+1$\\\\Divide both sides by 2 \\\\$(x^2-2x+1)=-\dfrac{1}{2}$\\\\Express the left side as a perfect square\\\\$(x-1)^2=-\dfrac{1}{2}$\\\\Take the square-root of both sides\\\\$x-1=\pm \dfrac{\sqrt{2}}{2}\;i$\\\\$x=1\pm\dfrac{\sqrt{2}}{2}\;i i$\\\\Therefore, the solution set is\\\\$\left\{1-\dfrac{\sqrt{2}}{2},1+\dfrac{\sqrt{2}}{2} \right\}$

47.)To solve the equation\\\\$ax^2+bx+c=0$\\\\The quadratic formula is\\\\

$x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$\\\\a = 1\\\\b = 3 \\\\c= -1\\\\$t=\dfrac{-3\pm \sqrt{3^2-4(1)(-1)}}{2(1)}$\\\\$t=\dfrac{-3\pm \sqrt{13}}{2}$\\\\Therefore, the solution set is\\\\$\left\{ \dfrac{-3-\sqrt{13}}{2}, \dfrac{-3+\sqrt{13}}{2} \right\}$48.)

a = 1\\\\b = 2\\\\c = -1\\\\$t=\dfrac{-2\pm \sqrt{2^2-4(1)(-1)}}{2(1)}$\\\\$t=\dfrac{-2\pm \sqrt{8}}{2}$\\\\Simplify\\\\$t=-1\pm \sqrt{2}$\\\\Therefore, the solution set is\\\\$\left\{ -1-\sqrt{2}, -1+\sqrt{2} \right\}$49.) a= 1\\\\b = 1\\\\c = 1\\\\$s=\dfrac{-1\pm \sqrt{1^2-4(1)(1)}}{2(1)}$\\\\$s=\dfrac{-1\pm \sqrt{3}i}{2}$\\\\Therefore, the solution set is\\\\$\left\{ \dfrac{-1-\sqrt{3}i}{2}, \dfrac{-1+\sqrt{3}i}{2} \right\}$

50.)a = 2\\\\b = 5\\\\c= 2\\\\$s=\dfrac{-5\pm \sqrt{5^2-4(2)(2)}}{2(2)}$\\\\$s=\dfrac{-5 \pm \sqrt{9}}{4}$\\\\$s=\dfrac{-5\pm 3}{4}$\\\\Therefore, the solution set is\\\\$\left\{ -2, -\dfrac{1}{2} \right\}$51.)a = 3\\\\b = -3\\\\c = -4\\\\$x=\dfrac{-(-3)\pm \sqrt{(-3)^2-4(3)(-4)}}{2(3)}$\\\\$x=\dfrac{3\pm \sqrt{57}}{2(3)}$\\\\$x=\dfrac{3\pm \sqrt{57}}{6}$\\\\Therefore, the solution set is\\\\$\left\{ \dfrac{3-\sqrt{57}}{6}, \dfrac{3+\sqrt{57}}{6} \right\}$52.)

a = 4\\\\b = -2\\\\c = -7\\\\$x=\dfrac{-(-2)\pm \sqrt{(-2)^2-4(4)(-7)}{2(4)}$\\\\$x=\dfrac{2\pm 2\sqrt{29}}{8}$\\\\Simplify\\\\$x=\dfrac{1\pm \sqrt{29}}{4}$\\\\Therefore, the solution set is\\\\$\left\{ \dfrac{1-\sqrt{29}}{4}, \dfrac{1+\sqrt{29}}{4} \right\}$53.)a = 1\\\\b = -2\\\\c = 17\\\\$x=\dfrac{-(-2)\pm \sqrt{(-2)^2-4(1)(17)}}{2(1)}$\\\\$x=\dfrac{2\pm 8i}{2}$\\\\Simplify further\\\\$x=1\pm 4i$\\\\Therefore, the solution set is\\\\$\left\{ 1-4i, 1+4i \right\}$54.)a = 4\\\\b = 7\\\\c = 8\\\\$m=\dfrac{-7\pm \sqrt{7^2-4(4)(8)}}{2(4)}$\\\\$m=\dfrarc{-7\pm \sqrt{79}i}{8}$\\\\Therefore, the solution set is\\\\$\left\{ \dfrac{-7-\sqrt{79}i}{8}, \dfrac{-7+\sqrt{79}i}{8}\right\}$55.)a = 5\\\\b = 7\\\\c = -3\\\\$x=\dfrac{-7\pm \sqrt{7^2-4(5)(-3)}}{2(5)}$\\\\$x=\dfrac{-7\pm \sqrt{109}}{10}$\\\\Therefore, the solution set is\\\\$\left\{ \dfrac{-7-\sqrt{109}}{10}, \dfrac{-7+\sqrt{109}}{10} \right\}$56.)a = 3\\\\b = 5\\\\c = 11 \\\\$x=\dfrac{-5\pm \sqrt{5^2-2(3)(11)}}{2(3)}$\\\\$x=\dfrac{-5\pm \sqrt{107}i}{6}$\\\\Therefore, the solution set is\\\\$\left\{ \dfrac{-5-\sqrt{107}i}{6}, \dfrac{-5+\sqrt{107}i}{6} \right\}$

[skip ]59.)Factor the quadratic equation\\\\

$v^2-8v-20=0$\\\\$(v+2)(v-10)=0$\\\\$v=-2$ or $v=10$Therefore, the solution set is\\\\$\left\{ -2,10 \right\}$Use quadratic formula\\\\a = 1\\\\b = -8\\\\c = 20\\\\$v=\dfrac{-(-8)\pm \sqrt{(-8)^2-4(1)(20)}}{2(1)}$\\\\Simplify\\\\$v=\dfrac{8\pm 4i}{2}$\\\\$v=4\pm 2i$\\\\Therefore, the solution set is\\\\$\left\{ 4-2i, 4+2i\right\}$61.)Factor the quadratic equation\\\\$t^2+5t-6=0$\\\\$(t-1)(t+6)=0$\\\\Equate each factor to zero\\\\$t = 1$ or $t= -6$\\\\Therefore, the solution set is\\\\$\left\{ -6,1 \right\}$62.) Factor the quadratic equation\\\\$t^2+5t+6=0$\\\\$(t+2)(t+3)=0$\\\\Equate each factor to zero\\\\$t=-2$ or $t=-3$\\\\Therefore, the solution set is\\\\$\left\{ -3, -2 \right\}$63.)Take the square root of both sides\\\\$\sqrt{(x+3)^2}=\sqrt{16}$\\\\$x+3=\pm 4$\\\\$x=-3\pm 4$\\\\$x=-7$ or $x=1$\\\\Therefore, the solution set is\\\\$\left\{ -7, 1 \right\}$64.) Take the square root of both sides\\\\$\sqrt{(x+3)^2}=\sqrt{-16}$\\\\$x+3=\pm 4i$\\\\$x=-3\pm 4i$\\\\Therefore, the solution set is\\\\$\left\{ -3-4i, -3+4i \right\}$