Question

Solve by completing the square :

$(c-2)(c+8)=11$

Short answer

The required value of$c$is$-9,3$

Step-by-step solution

Given information

$(c-2)(c+8)=11$

Calculation

$$\begin{gathered} (c-2)(c+8)=11 \\ \Rightarrow c(c+8)-2(c+8)=11 \\ \Rightarrow c^2+8c-2c-16=11 \\ \Rightarrow c^2+6c=11+16 \\ \Rightarrow c^2+6c=27 \\ \Rightarrow c^2+6c+{(\frac{1}{2}\times 6)}^2=27+9 \\ \Rightarrow c^2+6c+9=27+9 \\ \Rightarrow {(c+3)}^2=36\Rightarrow c+3=\pm \sqrt{36} \\ \Rightarrow c+3=\pm 6 \\ \Rightarrow c=-3\pm 6 \\ =-3-6,-3+6 \\ =-9,3 \end{gathered}$$

The required value of$c$is$-9,3$