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Chapter 0: Problem 108

Solve each equation, rounding your answer to four significant digits where necessary. $$ x^{2}-1=0 $$

Short Answer

Expert verified
The solutions to the equation \(x^2-1=0\) are \(x=-1\) and \(x=1\).

Step by step solution

01

Identify the equation

The given equation is \(x^2-1=0\)
02

Factor the equation

We can factor this equation using the difference of squares method: \((x+1)(x-1)=0\)
03

Determine the possible values for x

Now we'll set each factor equal to 0 and solve for x: \((x+1)=0\) gives us \(x=-1\) \((x-1)=0\) gives us \(x=1\)
04

Round the answers to four significant digits if necessary

Since both answers, -1 and 1, are integers, there is no need to round to four significant digits. Therefore, we have our final solutions: \(x=-1\) and \(x=1\).

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