Show that the equation x3 + 8x = 30 has a solution of 2.2 and 2.3

Question

Im unsure of how to work this out, please help me

Answer 1

Actually, this question should contain "...solution between x=2.2 and 2.3".

Substitute x=2.2 in x^3+8x-30=-1.752

Now substitute x=2.3: x^3+8x-30=0.567.

The sign of the first result is negative so x=2.2 in x^3+8x gives an answer <30 and the sign of the second result is positive so x=2.3 gives the answer >30. That proves that x must be in between 2.2 and 2.3. (The answer is approximately 2.2761.)