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Chapter 0: Problem 113

Solve each equation, rounding your answer to four significant digits where necessary. $$ x^{5}+32=0 $$

Short Answer

Expert verified
The solution to the equation \(x^5 + 32 = 0\) is \(x = -2\).

Step by step solution

01

Set the equation to the standard form

This equation is already in standard form, which is: \(x^5 + 32 = 0\)
02

Solve for x

As we have a fifth degree polynomial equation, isolating x may require factoring, but in this case, we can easily subtract 32 from both sides to isolate the term with x: \(x^5 = -32\) Now, to find the value of x, take the fifth root of both sides: \(x = \sqrt[5]{-32}\) Calculate the value: \(x = -2\)
03

Check the solution

To ensure that the solution is correct, plug the value of x back into the original equation and verify if it equals zero: \((-2)^5 + 32 = -32 + 32 = 0\) The equation holds true with our solution, so x = -2 is correct.
04

Round the answer

In this case, we do not need to round the answer because it is already a whole number with a single digit. Therefore, the final solution to the given equation is: \(x = -2\)

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