<s>[INST] How to solve this simple equation $\frac{46}{y} + y = 25$? How do I solve this simple equation?  $\frac{46}{y} + y = 25$
I know that the answer is $2$, but how do I arrive at that? 
 [/INST] $$\frac{46}{y}+y = 25$$
Here, assuming $y \neq 0$, you can multiply both sides of the equation by $y$, yielding
$$46+y^2 = 25y$$
$$y^2-25y+46 = 0$$
Here, you can solve the quadratic equation  by factoring, completing the square, or the Quadratic Formula, but the first way is the simplest, considering $a = 1$:
$$(y+y_1)(y+y_2) = 0$$
The key here is to ask yourself: which two numbers multiply to give $+46$ and add to give $-25$? Clearly the two numbers must be negative, and you can figure out they’re $-23$ and $-2$. So, the factored equation becomes
$$(y-23)(y-2) = 0$$
Setting either factor equal to $0$ yields

*

*$$y-23 = 0 \iff y = 23$$

*$$y-2 = 0 \iff y = 2$$
You could also use the Quadratic Formula if desired:

$$ax^2+bx+c = 0 \iff x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}$$
$$y = \frac{-(-25)\pm\sqrt{(-25)^2-4(1)(46)}}{2(1)} = \frac{25\pm\sqrt{441}}{2} = \frac{25\pm 21}{2}$$
$$y = 23; \quad y = 2$$

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