Name:                                    Date:

Solve the following quadratic equations:

Question 1: $-{\Large\frac{120}{u-2}}+{\Large\frac{49}{u-1}}=15$	Question 2: ${\Large\frac{102s-30}{7s+3}}=5s+2$
Question 3: $(z+6)^2+(z+7)^2=(z+8)^2$	Question 4: $-{\Large\frac{3}{f+1}}+{\Large\frac{40}{f+2}}=20$
Question 5: ${\Large\frac{58d+19}{2d+3}}=9d-2$	Question 6: ${\Large\frac{70v+63}{4v+9}}=7v+2$
Question 7: ${\Large\frac{10}{m}}+{\Large\frac{9}{m+1}}=12$	Question 8: $(j+4)^2+(3j+15)^2=(4j+13)^2$
Question 9: $(q+1)^2+(2q+1)^2=(2q+3)^2$	Question 10: $13a^2-55a=-5a-11a^2-25$
Question 11: $-{\Large\frac{49}{c+2}}+{\Large\frac{108}{c+3}}=10$	Question 12: ${\Large\frac{135k-50}{9k+7}}=3k+2$
Question 13: $18t^2+13t=11t+3t^2+45$	Question 14: $11n^2-38n=-7n+5n^2-35$
Question 15: $(r-3)^2+(2r-4)^2=(3r-11)^2$	Question 16: $32y^2+13y=8y-10y^2+63$

Answers

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