Is $ \forall\space x \in \mathbb{R} \space \exists \space y \in \mathbb{R} \space(x+y^2=10)$ true or false? 
Given the expression $\forall\space x \in \mathbb{R} \space \exists \space y \in \mathbb{R}\space(x+y^2=10)$ tell what is its logical value?

When I look to an expression with quantifiers, I try to translator into current language. In this case my atempt was "for each real number $x$ there is a real number $y$ that satisfy $x+y^2=10$". Or " for a given real number $x$ there is a real number $y$ that satisfy $x+y^2=10$".
Can I take from the previous thought that $y=\sqrt{10-x} \space$ ?(for a given $x$...there is a $y$).
Thanks

As you can see, there is no $y \in \mathbb{R}$ for $x>10$ which satisfies the equation

