How do I isolate X in this equation?

You’ve only got half the answer I’m afraid. x= -1.618 is also a solution (in fact x= 0.618 and -1.618 at the same time).

@Lightlyseared My calculator only gave 0.618, but it probably assumed that there was only one answer.

My question was how to get X. To be honest, I really don’t care what X is.

This a quadratic, because there’s an x^2 term, an x term, and a constant term. Start by rearranging in standard form:
x^2 + x – 1 = 0
...and then solve using quadratic formula or by completing the square. Can you take it from there?

Man, I forgot about the quadradic formula. To think I took advanced calculus in college, and I’m already forgetting algebra. Frak.

Build him up in front of his peers. Badmouth his peers in the same speech. Ought to be enough to get the other 25 letters to start avoiding him. Persist, and X will be permanently isolated.

What grade are you in? I mean no disrespect, but I am a bit surprised that someone who knows how to handle a sophisticated concept like the pigeonhole principle is unfamiliar with the solution of quadratic equations.

x^2 + x -1 = 0
x^2 + x + (¼ – ¼) – 1 = 0
(x^2 + x + ¼) – 5/4 = 0
(x + ½)^2 = 5/4
x + ½ = +/-sqrt(5/4)
x = -½ +/-sqrt(5/4) = 1.618…, .618…

The first of these numbers is the golden ratio, denoted by phi (as in your name), and the second is the inverse of the golden ratio, denoted by capital phi.

Correction: The first term should be -1.618.., which is the negative of the golden ratio.

@everyone In hindsight, I really should have been able to solve this. Really should have should have been able to. In fact, I can’t believe I forgot how to do this. But that is how summer zaps the brain. Summing infinite series, all of that stuff, I can do because that is the math that I did over the summer. But not one of those problems required quadratic equations. Wow. Face palms in shame

I agree with @gasman and @LostInParadise. I will tell you general rule. You need to re-arrange any quadratic equation in this format, and put values of the corresponding constants.

General form of a quadratic equation : ax^2 + bx + c = 0
Two values of x are :
x = [- b +/- Square root (b^2 – 4ac)] / (2a) ...use +/- to get two values

If the equation is relatively simpler, use factorization method as @LostInParadise has shown. Personally, I will use factorization when constants a,b,c are integers. In other cases, it is more easier to find roots using the above formula.

Generally, you will get as many number of values for x, the variable, as the highest degree in the equation. For quadratic equation, the highest degree is two, so you can get two values for x. For cubic equation, there will be three values for x, and so on.

@prasad I know/knew all of that, but I forgot, and now I remember. This whole question was one giant brain lapse on my part.

If you really want to cheat :-) use Wolfram Alpha

http://www.wolframalpha.com/input/?i=1+%3D+x+%2B+x%5E2