Question

6 solve the following quadratic equations a) x^2+7x+12=0 b) x² -14=5x

Answer 1

Let's begin by identifying key information given to us:

a)

$\begin{gathered} x^2+7x+12=0 \\ \text{Factorise we have:} \\ x^2+4x+3x+12=0 \\ x(x+4)+3(x+4)=0 \\ (x+4)(x+3)=0 \\ x+4=0,x+3=0 \\ \Rightarrow x=-4,x=-3 \end{gathered}$

b)

$\begin{gathered} x^{2}-14=5x​ \\ \text{Subtract ''5x'' from both sides to make the equation in the standard form. We have:} \\ x^{2}-5x-14=5x​-5x \\ x^{2}-5x-14=0 \\ \text{Factorising, we have:} \\ x^2+2x-7x-14=0 \\ x(x+2)-7(x+2)=0 \\ (x+2)(x-7)=0 \\ x+2=0,x-7=0 \\ \Rightarrow x=-2,x=7 \end{gathered}$