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Solving Quadratic Equations by Factorising 4 worksheet

Name:                                    Date:
Solve the following quadratic equations:

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

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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
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