How to solve a quadratic which has a term with a square root over the variable?
Hello, AaPa!
How to solve: .$\displaystyle x^2+2x+3+4\sqrt{x} \:=\:0$
This is not a quadratic.
You have: .$\displaystyle x^2 + 2x + 4\sqrt{x} + 3 \:=\:0$
Let $\displaystyle \sqrt{x}=u \quad\Rightarrow\quad x = u^2$
The equation becomes: .$\displaystyle u^4 + 2u^2 + 4u + 3 \:=\:0$
And you have a quartic to solve.