Name:                                    Date:

Solve the following quadratic equations:

Question 1: $(t+1)^2+(2t+4)^2=(3t+1)^2$	Question 2: ${\Large\frac{54w-21}{3w+4}}=4w+1$
Question 3: $(j+2)^2+(2j+3)^2=(2j+5)^2$	Question 4: ${\Large\frac{56y-18}{5y+9}}=2y+1$
Question 5: $27n^2-7n=-3n-5n^2+15$	Question 6: $-{\Large\frac{88}{c-2}}+{\Large\frac{35}{c-1}}=12$
Question 7: ${\Large\frac{138k+37}{2k+9}}=9k+1$	Question 8: $57v^2-100v=-7v+3v^2-40$
Question 9: $-{\Large\frac{64}{z+2}}+{\Large\frac{143}{z+3}}=15$	Question 10: ${\Large\frac{-140e-54}{4e-9}}=6e-1$
Question 11: $24a^2-89a=-2a-4a^2-54$	Question 12: ${\Large\frac{9}{g+1}}+{\Large\frac{13}{g+2}}=8$
Question 13: $-{\Large\frac{12}{d}}+{\Large\frac{1}{d+1}}=20$	Question 14: $(u+4)^2+(3u+15)^2=(4u+13)^2$
Question 15: $16s^2+54s=10s+4s^2+45$	Question 16: $(p+6)^2+(p+7)^2=(p+8)^2$

Answers

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