To solve quadratic equation using factorisation
(a)
[tex]\begin{gathered} x^2\text{ -x = 56} \\ x^2-x-56\text{ = 0} \\ x^2-8x+7x-56=0 \\ x(x-8)+7(x-8)=0_{} \\ (x-8)(x+7)=0 \\ x-8=0\text{ or x+7=0} \\ x=8\text{ or x = -7} \end{gathered}[/tex]
(b)
[tex]\begin{gathered} x^2\text{ = }3x\text{ + 28} \\ x^2-3x-28\text{ = 0} \\ x^2-7x+4x-28=0 \\ x(x-7)+4(x-7)=0_{} \\ (x-7)(x+4)=0 \\ x-7=0\text{ or x+4=0} \\ x=7\text{ or x = -}4 \end{gathered}[/tex]
(c)
[tex]\begin{gathered} \frac{1}{2b}\text{ = }\frac{3}{5b}+3 \\ \text{collect like terms} \\ \frac{1}{2b}\text{ - }\frac{3}{5b}\text{ = 3} \\ \frac{5\text{ - 6}}{10b}\text{ = 3} \\ \frac{-1}{10b}\text{ = 3} \\ -1\text{ = 10b x 3} \\ -1\text{ = 30b} \\ \text{divide oth side by 30b} \\ b=\frac{-1}{30}\text{ } \end{gathered}[/tex]
