Richard Z.

# Can 2^x = x^2 be solved explicitly? I can see that {2,4} are solutions, but the calculator shows a third solution, x=-0.7666647.

2x = x2
How would you solve this?

## 2 Answers By Expert Tutors

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Rigorous Physics Tutoring Christopher R.

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I would have used Newton's Method to solve this problem. Base upon what is listed on what level math the student is taking, I don't know if he is at the Calculus level or above.
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11/24/14 Francisco P.

Are there any other methods besides graphing that you know of, Christopher?
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11/24/14 Christopher R.

tutor
Perhaps, your right. This would be a calculus problem if you had to solve this problem other than graphing. However, one can setup this problem as a function being f(x)=2- xand make a table containing intelligent guesses to find what values of x would make the function equal to zero. Then use interpolation to find the approximate value of x. For example, let x=0 in which makes f(0)=1 and x=-1 in which makes f(-1)=1/2-1=-1/2. I think you can see what I'm saying about how one could use interpolation to find some approximate value of x being in between x=0 and x=-1 to make the original equation to be true.

Moreover, this could be one way to show the student on how to do the problem if he is taking Algebra II.
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11/24/14 Francisco P.

I didn't think of that.  Thanks and happy tutoring.
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11/25/14 Christopher R.

tutor
Your welcome, you could see that I didn't initially think of that either... Lol. Thanks for your answer and happy tutoring to you also.
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11/25/14

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