Name:                                    Date:

Solve the following quadratic equations:

Question 1: $(d+1)^2+(2d+4)^2=(3d+1)^2$	Question 2: $-{\Large\frac{1}{s+1}}+{\Large\frac{30}{s+2}}=20$
Question 3: ${\Large\frac{-9q+19}{7q+4}}=2q-2$	Question 4: $(f-3)^2+(f-2)^2=(f-1)^2$
Question 5: ${\Large\frac{60g+45}{6g+5}}=9g+2$	Question 6: $19w^2-12w=-11w+7w^2+35$
Question 7: $(u-4)^2+(2u-9)^2=(2u-7)^2$	Question 8: $-{\Large\frac{6}{n-2}}-{\Large\frac{1}{n-1}}=10$
Question 9: $19r^2-100r=-3r-23r^2-56$	Question 10: ${\Large\frac{-94z-29}{2z-3}}=8z-2$
Question 11: $23b^2-46b=-5b+3b^2-20$	Question 12: $-{\Large\frac{130}{v+2}}+{\Large\frac{234}{v+3}}=15$
Question 13: $(k+6)^2+(3k+21)^2=(4k+21)^2$	Question 14: ${\Large\frac{12}{t}}-{\Large\frac{7}{t+1}}=12$
Question 15: ${\Large\frac{-72e-35}{4e-5}}=6e+2$	Question 16: $20a^2+4a=3a-36a^2+42$

Answers

Question 1: $4(d+1)(d-4)=0$ $\implies d=-1 , d=4$	Question 2: $(4s+3)(5s+4)=0$ $\implies s=-{\Large\frac{3}{4}} , s=-{\Large\frac{4}{5}}$
Question 3: $(7q-9)(2q+3)=0$ $\implies q={\Large\frac{9}{7}} , q=-{\Large\frac{3}{2}}$	Question 4: $(f-6)(f-2)=0$ $\implies f=6 , f=2$
Question 5: $(6g-5)(9g+7)=0$ $\implies g={\Large\frac{5}{6}} , g=-{\Large\frac{7}{9}}$	Question 6: $(3w+5)(4w-7)=0$ $\implies w=-{\Large\frac{5}{3}} , w={\Large\frac{7}{4}}$
Question 7: $(u-4)(u-12)=0$ $\implies u=4 , u=12$	Question 8: $(2n-3)(5n-4)=0$ $\implies n={\Large\frac{3}{2}} , n={\Large\frac{4}{5}}$
Question 9: $(7r-8)(6r-7)=0$ $\implies r={\Large\frac{8}{7}} , r={\Large\frac{7}{6}}$	Question 10: $(2z+7)(8z+5)=0$ $\implies z=-{\Large\frac{7}{2}} , z=-{\Large\frac{5}{8}}$
Question 11: $(4b-5)(5b-4)=0$ $\implies b={\Large\frac{5}{4}} , b={\Large\frac{4}{5}}$	Question 12: $(5v-3)(3v-4)=0$ $\implies v={\Large\frac{3}{5}} , v={\Large\frac{4}{3}}$
Question 13: $6(k+6)(k-1)=0$ $\implies k=-6 , k=1$	Question 14: $(3t+4)(4t-3)=0$ $\implies t=-{\Large\frac{4}{3}} , t={\Large\frac{3}{4}}$
Question 15: $(4e+5)(6e+5)=0$ $\implies e=-{\Large\frac{5}{4}} , e=-{\Large\frac{5}{6}}$	Question 16: $(8a+7)(7a-6)=0$ $\implies a=-{\Large\frac{7}{8}} , a={\Large\frac{6}{7}}$