Name:                                    Date:

Solve the following quadratic equations:

Question 1: $(y-3)^2+(2y-7)^2=(2y-5)^2$	Question 2: $44r^2+28r=7r+4r^2+27$
Question 3: $(k+6)^2+(k+7)^2=(k+8)^2$	Question 4: ${\Large\frac{-44v+30}{2v-5}}=6v+1$
Question 5: ${\Large\frac{-20u+12}{9u-8}}=5u+1$	Question 6: $24m^2-40m=-7m+4m^2-10$
Question 7: $-{\Large\frac{27}{e-2}}-{\Large\frac{7}{e-1}}=8$	Question 8: $(t+2)^2+(2t+6)^2=(3t+4)^2$
Question 9: $14q^2-74q=-12q-7q^2-45$	Question 10: $2s^2-64s=-7s-25s^2+40$
Question 11: ${\Large\frac{10}{j}}-{\Large\frac{15}{j+1}}=6$	Question 12: $-{\Large\frac{9}{p+1}}+{\Large\frac{78}{p+2}}=20$
Question 13: $-{\Large\frac{104}{f+2}}+{\Large\frac{187}{f+3}}=12$	Question 14: $(d+1)^2+(3d+6)^2=(4d+1)^2$
Question 15: ${\Large\frac{36h+68}{6h+5}}=7h+1$	Question 16: ${\Large\frac{120a+5}{8a+9}}=9a-1$

Answers

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