<s>[INST] Factoring out the expression I'm sorry, it must pretty basic, but...
How to factor out this expression $x^2 + 5x - 5 = 0$  ? 
(The method I normally use to factor expressions doesn't work there because when we factor expression above so that format will be $(ax + b)(qx + c)$ $b$ and $c$ definitely won't be integers, and method that I use only works when $b$ and $c$ are integers)
 [/INST] You can use completing square method to factorize it. 
Look at: 
$$x^2+5x-5=x^2+ 2x\times\frac{5}{2}+\frac{25}{4}-\frac{25}{4}-5=(x +\frac{5}{2})^2-(\sqrt\frac{45}{2})^2$$
Now use the fact that $a^2-b^2 = (a+b)(a-b)$, so:
$$x^2+ 5x -5 =(x +\frac{5}{2})^2-(\sqrt\frac{45}{2})^2 = (x+\frac{5}{2}+\sqrt\frac{45}{2})(x+\frac{5}{2}-\sqrt\frac{45}2)$$
which is your answer.
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