Question

Solve the equation. $$x^{2}=\frac{9}{25}$$

Short answer

The solutions of the given equation are: \(x= \frac{3}{5}\) or \(x= -\frac{3}{5}\)

Step-by-step solution

Analyze the equation

The given equation is \(x^{2} = \frac{9}{25}\). It is a typical quadratic function where the variable \(x\) is squared.

Take the square root of both sides

To find the value of \(x\), let's take the square root of both sides of the equation. This will give us two solutions, one positive, and one negative, since both a negative and positive number squared would yield the original number. So, we have \(x= \sqrt{\frac{9}{25}}\) or \(x= -\sqrt{\frac{9}{25}}\)

Calculate the square root of the fraction

Calculating the square root of the given fraction, we have \(x= \sqrt{\frac{9}{25}} = \frac{3}{5}\) or \(x= -\sqrt{\frac{9}{25}} = -\frac{3}{5}\)