Question

if root of x+6 =2x then what is the value of x

Answer 1

$$\begin{gathered} \left(\sqrt{x}+6\right)=2x \\ \Rightarrow \sqrt{x}=2x-6 \\ \Rightarrow {\left(\sqrt{x}\right)}^2={\left(2x-6\right)}^2\{\mathrm{squaring}\mathrm{both}\mathrm{sides}\} \\ \Rightarrow x=4x^2+36-24x \\ \Rightarrow 4x^2-25x+36=0 \\ \Rightarrow 4x^2-16x-9x+36=0 \\ \Rightarrow 4x\left(x-4\right)-9\left(x-4\right)=0 \\ \Rightarrow \left(4x-9\right)\left(x-4\right)=0 \\ \Rightarrow \left(4x-9\right)=0\mathrm{and}\left(x-4\right)=0 \\ \Rightarrow x=\frac{9}{4}\mathrm{and}x=4 \end{gathered}$$
Since $x=\frac{9}{4}$ does not satisfy the given solution, so x = 4