# Solve Difficult Equation: x = 4

• mazen_zone
In summary, the conversation discusses a difficult equation given by a friend and the difficulty of solving it algebraically. It is suggested to use calculators or Newton's method to solve it, but it is also noted that the solution may be complex and not easily expressed.

#### mazen_zone

hey all,

a friend gave me this equation and required that i solve it:

http://www.geocities.com/mazen_zone/Untitled.jpg

I could only solve it graphically and the answer was (x = 4),
so i wonder if there is an algebraic solution for it ?

I don't think there is any way to solve it algebraically.

With such equations, it's easy to create them, while terribly annoying to solve without calculators to solve it numerically for you. I think your friend may have caused you a headache for laughs

Last edited:
Mentallic said:
I don't think there is any way to solve it algebraically.

With such equations, it's easy to create them, while terribly annoying to solve without calculators to solve it numerically for you. I think your friend may have caused you a headache for laughs

lol yeah i guess...thanks anyway.

log it, make sqrt(x) the subject, square both sides, and I think that would give you a quadratic which is easy to solve.

edit: Sorry I just realized that's a dumb idea. Yeah, I don't think there's any way to solve it analytically.

Anyway, not with log and all. Since you have a sum of the two, the log would not apply in that sense.

Cheers

Calculators use Newton's method to solve equations (including this type of equations of course)
maybe that's the only analytic way to solve it, but i don't know how to use this method

"Algebraically" is a vague term. It is easy to see that if there is a rational answer then it must actually be integral, and in fact x is a square. This leads you to try 1,4 and get the answer (almost) immediately.

If there isn't such a nice easy to spot idea, then the solution is almost certainly going to be nasty, transcendental and impossible to write down in any nice way, so don't bother to try.