How can I solve x+2=exp(x) ?

Question

Can you please help me solve this equation I've been stuck for like 2 hours!

Answer 1

There's no exact answer in terms of standard functions. See the link below for some information. You can see from the plot that there are two solutions, one around x = -1.8 and one around x = 1.2. (You can prove that there are no more than two solutions by considering the derivatives.) You can use Newton's method to refine these; if f(x) = x + 2 - e^x, f '(x) = 1 - e^x. Start with the guesses above and iterate with x_(n+1) = x_n - f(x_n) / f '(x_n).



To 8 decimal places I get the answers as -1.84140566 and 1.14619322.

Answer 2

All answer are incorrect or in area suitable suited! The is a attempt besides the fact that if the equation holds. because of the fact the quotient x/x is given, the equation is defined for x=0, because of the fact the certainty, that there is a real minimize for x goint to 0 of x/x: limit_x->0 x/x=a million. So do away with the quotient a minimum of for x unequal 0. The equation now's x+x²=x². This equation could be rearranged through unique arithmetic operations. It supplies x=0. stupid or. What does is advise? The equation does not carry for x unequal 0. it quite is it. it may returned be simplified a million+x=x or a million=0, that's erroneous. For 0 is holds interior the stable style and interior the minimize attention: 0/0+0=a million+0 unequal 0. The equation does not be valid for any actual numbers!

Answer 3

Maybe you mean:

x + 2 = x^2?

I don't know what exp(x) means actually..

x^2 - x - 2 =0

(x-2)(x+1)=0

x= 2, -1



Have a great day! :-)

Answer 4

The equation x + 2 = e^x cannot be solved algebraically, because the left hand side is algebraic, but the right hand side is transcendental.

It can be solved graphically: x ≈ 1.14619...

Answer 5

x + 2 = x²

x² - 1/2x = 2 + (- 1/2)²

x² - 1/2x = 8/4 + 1/4

(x - 1/2)² = 9/4

x - 1/2 = ± 3/2



x = 3/2 + 1/2, x = 4/2, x = 2

x = - 3/2 + 1/2, = x - 2/2, x = - 1



Answer: x = 2, - 1