\( 50 x^{2}=70 \) What is one of the solutions to the given equation? \( \sqrt{\frac{7}{5}} \) \( \sqrt{\frac{5}{7}} \) \( \sqrt{20} \) \( 2 \sqrt{5} \)

To solve the equation \( 50 x^{2} = 70 \), we first simplify it. Dividing both sides by 50 gives us \( x^{2} = \frac{70}{50} \), which simplifies to \( x^{2} = \frac{7}{5} \). Taking the square root of both sides results in \( x = \pm \sqrt{\frac{7}{5}} \). Therefore, one of the solutions is \( \sqrt{\frac{7}{5}} \). Squaring the solution gives us verification! If \( x = \sqrt{\frac{7}{5}} \), then \( x^2 = \frac{7}{5} \), and substituting back into the original equation confirms that indeed \( 50 \left(\frac{7}{5}\right) = 70 \). This positive square root not only verifies consistency but also showcases the beauty of solving equations through mathematical properties!