Name:                                    Date:

Solve the following quadratic equations:

Question 1: ${\Large\frac{92b-46}{4b+3}}=6b+1$	Question 2: $(z+2)^2+(z+3)^2=(z+4)^2$
Question 3: $(r-5)^2+(3r-12)^2=(4r-23)^2$	Question 4: $31n^2-82n=-12n+7n^2-49$
Question 5: $4w^2-38w=-9w-2w^2-28$	Question 6: ${\Large\frac{-141s-51}{9s-5}}=5s-1$
Question 7: $-{\Large\frac{91}{t+2}}+{\Large\frac{153}{t+3}}=8$	Question 8: $37p^2-20p=-3p+7p^2+21$
Question 9: $(k+4)^2+(2k+7)^2=(2k+9)^2$	Question 10: ${\Large\frac{8}{u-2}}-{\Large\frac{9}{u-1}}=10$
Question 11: $9d^2-32d=-9d-9d^2+6$	Question 12: $(j+6)^2+(2j+14)^2=(3j+16)^2$
Question 13: ${\Large\frac{20}{g}}+{\Large\frac{9}{g+1}}=20$	Question 14: ${\Large\frac{-66e-40}{6e-5}}=3e+1$
Question 15: $-{\Large\frac{7}{q+1}}+{\Large\frac{44}{q+2}}=12$	Question 16: ${\Large\frac{134f+29}{2f+7}}=9f-1$

Answers

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