Name:                                    Date:

Solve the following quadratic equations:

Question 1: ${\Large\frac{-110d-57}{4d-9}}=7d+3$	Question 2: $36m^2-67m=-8m+6m^2-28$
Question 3: $(n+6)^2+(3n+21)^2=(4n+21)^2$	Question 4: $-{\Large\frac{3}{h-2}}+{\Large\frac{1}{h-1}}=8$
Question 5: ${\Large\frac{18r+0}{8r-3}}=5r+3$	Question 6: ${\Large\frac{-52y-12}{2y-3}}=4y-3$
Question 7: $(z+1)^2+(2z+1)^2=(2z+3)^2$	Question 8: $12s^2-79s=-4s-2s^2-54$
Question 9: $(g+2)^2+(g+3)^2=(g+4)^2$	Question 10: $3j^2-42j=-12j-13j^2+25$
Question 11: $-{\Large\frac{8}{c}}+{\Large\frac{45}{c+1}}=15$	Question 12: ${\Large\frac{-98e+49}{3e-8}}=8e-3$
Question 13: $59q^2-57q=-6q+5q^2+14$	Question 14: $(f-3)^2+(2f-4)^2=(3f-11)^2$
Question 15: $-{\Large\frac{63}{t+2}}+{\Large\frac{132}{t+3}}=10$	Question 16: $-{\Large\frac{49}{u+1}}+{\Large\frac{90}{u+2}}=6$

Answers

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