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Chapter 0: Problem 109

Solve each equation, rounding your answer to four significant digits where necessary. $$ x^{2}-\frac{4}{9}=0 $$

Short Answer

Expert verified
The short answer for the given equation is \(x = 卤\frac{2}{3}\).

Step by step solution

01

Add the constant to both sides

Add \(\frac{4}{9}\) to both sides of the equation to isolate the quadratic term: \[x^2-\frac{4}{9}+\frac{4}{9}=0+\frac{4}{9}\] Which simplifies to: \[x^2=\frac{4}{9}\]
02

Take the square root of both sides

To find the possible values of x, take the square root of both sides. Remember that there are two possible square roots: positive and negative. \[\sqrt{x^2}=\sqrt{\frac{4}{9}}\] This gives us: \[x=卤\frac{2}{3}\]
03

Round to four significant digits

Our solution is already expressed with two significant digits, so no further rounding is necessary. Thus, the final answer is: \[x=卤\frac{2}{3}\]

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