Question

The number of value(s) of $x$ satisfying the equation $(x+9{)}^2+8|x+9|+7=0$ is

Answer 1

$(x+9{)}^2+8|x+9|+7=0$
$\Rightarrow |x+9{|}^2+8|x+9|+7=0(\because |x^2|=|x{|}^2)$

Let $|x+9|=t$
$\Rightarrow t^2+8t+7=0$
$\Rightarrow t^2+7t+t+7=0$
$\Rightarrow (t+7)(t+1)=0$
$\Rightarrow t=-7,-1$
We know that $|x+9|\ge 0\Rightarrow t\ge 0$

Hence, no values of $x$ is possible.