How Can I Solve This Equation in Mathematica?

[Physics_rocks]

Hi ,

I'm trying to solve the following equation:
e^x=x^3 + x^2 -1/4* x -4

using this code :
NSolve[Exp[x] = x^3 + x^2 - 0.25 * x - 4, x]

but it doesn't work .

In addition I'm trying to solve it graphically by plotting the left and right functions simultaneously . but how ? with PLOT ?

And when I try with FindRoot , it also says that something is wrong :
FindRoot[Exp[x] == x^3 + x^2 - 0.25 * x - 4, {x, 0}]

can you please help ? thanks

 

[nbo10]

Hi ,

I'm trying to solve the following equation:
e^x=x^3 + x^2 -1/4* x -4

using this code :
NSolve[Exp[x] = x^3 + x^2 - 0.25 * x - 4, x]

but it doesn't work .

In addition I'm trying to solve it graphically by plotting the left and right functions simultaneously . but how ? with PLOT ?

And when I try with FindRoot , it also says that something is wrong :
FindRoot[Exp[x] == x^3 + x^2 - 0.25 * x - 4, {x, 0}]

can you please help ? thanks

I don't use mathematica any more but try something like

F[x_] = - Exp[x] + x^3 + x^2 - 0.25 * x - 4;
NSolve[F[x] == 0,x];
FingRoot[F[x] ==0,{x,0}];

 

[Dale]

NSolve[Exp[x] = x^3 + x^2 - 0.25 * x - 4, x]

Here there are two problems. First, you need to use == instead of = and second NSolve is for solving polynomials and won't work for your expression. Use FindRoot instead.

In addition I'm trying to solve it graphically by plotting the left and right functions simultaneously . but how ? with PLOT ?

This is a good approach in general, one I usually use when I cannot easily solve something. Use Plot[{Exp[x], x^3 + x^2 - 0.25*x - 4}, {x, 1, 5}] and you can clearly see that there are two solutions, one near x=2 and one near x=5.

And when I try with FindRoot , it also says that something is wrong :
FindRoot[Exp[x] == x^3 + x^2 - 0.25 * x - 4, {x, 0}]

Remember, FindRoot is a numerical search that depends on the starting position. If you do the Plot above and know that the intersections are near x=2 and x=5 then use those as your starting points: FindRoot[Exp[x] == x^3 + x^2 - 0.25*x - 4, {x, 2}] gives x->1.98666
FindRoot[Exp[x] == x^3 + x^2 - 0.25*x - 4, {x, 5}] gives x->4.93916