Question

Solve quadratic equations of the form $x^2+bx+c=0$by completing the square.

In the following exercises , solve by completing the square.

$(x+6)(x-2)=9$

Short answer

The required value of$x$is$3,-7$

Step-by-step solution

Given information

$(x+6)(x-2)=9$

Calculation

$$\begin{gathered} (x+6)(x-2)=9 \\ \Rightarrow x(x-2)+6(x-2)=9 \\ \Rightarrow x^2-2x+6x-12=9 \\ \Rightarrow x^2+4x-12=9 \\ \Rightarrow x^2+4x=9+12 \\ \Rightarrow x^2+4x=21 \\ \Rightarrow x^2+4x+{(\frac{1}{2}\times 4)}^2=21\Rightarrow x^2+4x+4=21+4 \\ \Rightarrow {(x+2)}^2=25\Rightarrow x+2=\pm \sqrt{25}=\pm 5 \\ \Rightarrow x=-2\pm 5 \\ =-2+5,-2-5 \\ =3,-7 \end{gathered}$$

The required value of$x$is$3,-7$