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Chapter 0: Problem 110

Solve each equation, rounding your answer to four significant digits where necessary. $$ x^{2}-\frac{1}{10}=0 $$

Short Answer

Expert verified
The solutions for the equation \(x^2 - \frac{1}{10} = 0\) are approximately \(x_1 \approx 0.3162\) and \(x_2 \approx -0.3162\).

Step by step solution

01

Move the fraction to the other side of the equation

To do this, we can add \(\frac{1}{10}\) to both sides of the equation: \(x^2 = \frac{1}{10}\)
02

Take the square root of both sides of the equation

To find the value of x, we can take the square root of both sides of the equation. It麓s important to remember that when taking the square root of a variable raised to the power of 2, we will end up with two possible solutions (positive and negative values). \(\sqrt{x^2} = \pm\sqrt{\frac{1}{10}}\)
03

Evaluate the square root

Now we need to determine the numerical value of the square root. \(x = \pm\sqrt{\frac{1}{10}}\)
04

Simplify the square root

First, convert the fraction to a decimal. \(\frac{1}{10} = 0.1\) Then, find the square root of the decimal. \(x = \pm \sqrt{0.1}\)
05

Round the answer to four significant digits

Calculate the positive square root of 0.1, and round the answer to four significant digits. \(x_1 = +\sqrt{0.1} \approx 0.3162\) Calculate the negative square root of 0.1, and round the answer to four significant digits. \(x_2 = -\sqrt{0.1} \approx -0.3162\) The two solutions for x are approximately 0.3162 and -0.3162.

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Most popular questions from this chapter

By any method, determine all possible real solutions of each equation Check your answers by substitution. \(2 x^{2}-x-3=0\)

\(\left(x^{3}-2 x^{2}+4\right)\left(3 x^{2}-x+2\right)\)

Find all possible real solutions of each equation \(y^{3}+3 y^{2}+3 y+2=0\)

By any method, determine all possible real solutions of each equation Check your answers by substitution. \(-\frac{1}{2} x^{2}-\frac{1}{2} x+1=0\)

Convert each expression in Exercises into its technology formula equivalent as in the table in the text.\(2.1 x^{-3}-x^{-1}+\frac{x^{2}-3}{2}\)
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