Final answer:
The equation x^3 - 5x = 59 is solved by trial and improvement, testing values between 4 and 5, and finding which value of x satisfies the equation when rounded to one decimal place.
Step-by-step explanation:
The student is asking how to find a solution to the equation x^3 - 5x = 59 using trial and improvement. We know that the solution lies between 4 and 5. To solve this, we can test values within that range to see which value of x makes the equation true when rounded to one decimal place.
First, plug in x = 4:
(4)^3 - 5(4) = 64 - 20 = 44, which is less than 59.
Next, plug in x = 5:
(5)^3 - 5(5) = 125 - 25 = 100, which is greater than 59.
Since 59 is between 44 and 100, we know that the solution is indeed between 4 and 5. By further trial and closer approximations (4.1, 4.2, 4.3, etc.), we can hone in on the exact value to one decimal place.