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.

$(x-2)(x-6)=5$

Short answer

The required value of$x$is$7,1$

Step-by-step solution

Given information

$(x-2)(x-6)=5$

Calculation

$$\begin{gathered} (x-2)(x-6)=5 \\ \Rightarrow x(x-6)-2(x-6)=5 \\ \Rightarrow x^2-6x-2x+12=5 \\ \Rightarrow x^2-8x=5-12 \\ \Rightarrow x^2-8x=-7 \\ \Rightarrow x^2-8x+(\frac{1}{2}\times {(-8))}^2=-7+16 \\ \Rightarrow x^2-8x+16=-7+16 \\ \Rightarrow {(x-4)}^2=9\Rightarrow x-4=\pm \sqrt{9}=\pm 3 \\ \Rightarrow x=4\pm 3 \\ =4+3,4-3 \\ =7,1 \end{gathered}$$

The required value of$x$is$7,1$