Is This Answers Correct Or Not?

A good way to check it is to try out 2.38 and 2.39:

(2.38)^3 + 2.38 ≈ 15.86 < 16
(2.39)^3 + 2.39 ≈ 16.04 > 16.

Thus, the solution lies on (2.38, 2.39).

To show that the solution correctly rounds to x = 2.39, rather than rounding down to 2.38, you can show that a solution exists on (2.385, 2.39). We have:

(2.385)^3 + 2.385 ≈ 15.95 < 16.

Thus, a solution exists on (2.385, 2.39) and you are correct!

I hope this helps!

Since 2.4 would go over to 16.23, and you are only going 2 decimals places, your answer is slightly over, but very close.

3 places would give 2.387

*presses calculator* yup, 2.39 is correct :)

Yes, your answer is right!
x = 2.39
p.s. believe in yourself, that's what matters most!

x³ + x

(2)³ + (2) = 10
(3)³ + (3) = 30

Linear interpolation estimate increment = (16 - 10) / (30 - 10) = 0.3

(2 + 0.3)³ + (2 + 0.3)
= (2.3)³ + (2.3)
= 14.467

Linear interpolation estimate increment = (16 - 14.467) / (30 - 14.467) ≈ 0.09869

(2.3 + 0.09869)³ + (2.3 + 0.09869)
= (2.39869)³ + (2.39869)
≈ 16.20007

Linear interpolation estimate increment = (16 - 16.20007) / (30 - 16.20007) ≈ -0.01450

(2.39869 + -0.01450)³ + (2.39869 + -0.01450)
= (2.38419)³ + (2.38419)
≈ 15.93679

Linear interpolation estimate increment = (16 - 15.93679) / (30 - 15.93679) ≈ 0.00449

(2.38419 + 0.00449)³ + (2.38419 + 0.00449)
= (2.38868)³ + (2.38868)
≈ 16.01799

Linear interpolation estimate increment = (16 - 16.01799) / (30 - 16.01799) ≈ -0.00129

(2.38868 + -0.00129)³ + (2.38868 + -0.00129)
= (2.38739)³ + (2.38739)
≈ 15.99463

x is between 2.38739 and 2.38868.
Therefore x is 2.39 to two decimal places.

To continue for third decimal place,
Linear interpolation estimate increment = (16 - 15.99463) / (30 - 15.99463) ≈ 0.00038

(2.38739 + 0.00038)³ + (2.38739 + 0.00038)
= (2.38777)³ + (2.38777)
≈ 16.00151

Linear interpolation estimate increment = (16 - 16.00151) / (30 - 16.00151) ≈ -0.00011

(2.38777 + -0.00011)³ + (2.38777 + -0.00011)
= (2.38766)³ + (2.38766)
≈ 15.99952

x is between 2.38766 and 2.38777.
Therefore x is 2.388 to three decimal places.

To continue for fourth decimal place,
Linear interpolation estimate increment = (16 - 15.99952) / (30 - 15.99952) ≈ -0.00003

(2.38766 + -0.00003)³ + (2.38766 + -0.00003)
= (2.38769)³ + (2.38769)
≈ 16.00006

x is between 2.38766 and 2.38769.
Therefore x is 2.3877 to four decimal places.

2.388 = 16.00567