Squared like times 10

$\begin{aligned} \left(1 + \dfrac x{10} \right)^2 & = 10 + x \\ \Rightarrow \left(\dfrac{x + 10}{10}\right)^2 & =10 + x \\ \Rightarrow (x + 10)^2 & = 100(10 + x) \\ \Rightarrow x^2 + 20x + 100 & = 1000+ 100x \\ \Rightarrow x^2-80x -900 & = 0 \\ \Rightarrow x^2 -90x + 10x - 900 & = 0 \\ \Rightarrow x(x - 90) + 10(x - 90) & = 0 \\ \Rightarrow (x -90)(x +10) & = 0 \\ \end{aligned}$

Hence the answer is $x = 90$ or $x = -10$

$(10+x)^2=100(10+x)$

If $10+x$ does not equal to $0$ , then $10+x=100,x=90$

If $10+x$ equals to $0$ , then $x=-10$

Hence, the answer is $-10,90$

$(1+\frac{x}{10})^2=10+x \implies (10+x)^2=10^2(10+x)=10^2+2 \times 10x+x^2=100(10+x)=100+20x+x^2=1000+100x \implies x^2-80x-900=0$

$\frac{-(-80) \pm \sqrt{(-80)^2-4 \times 1 \times -900}}{2 \times 1}=\frac{80 \pm \sqrt{6400-(-3600)}}{2}=\frac{80 \pm \sqrt{6400+3600}}{2}=\frac{80 \pm \sqrt{10000}}{2}=\frac{80 \pm 100}{2}$

So the answer is $\boxed{\large{-10,90}}$