\( 0=\frac{1}{10} x^{2}-10 \) The solutions are \( x= \) and \( x=\square \)

To solve the equation \( 0 = \frac{1}{10} x^{2} - 10 \), you can first multiply everything by 10 to eliminate the fraction. This gives you \( 0 = x^{2} - 100 \). Now, rearranging it, we have \( x^{2} = 100 \). Taking the square root of both sides, we get \( x = 10 \) and \( x = -10 \). So the solutions are \( x = 10 \) and \( x = -10 \). Now, isn’t it fascinating how quadratics pop up in everyday life? For example, projectile motion is often modeled with quadratic equations, enabling engineers to design safer roller coasters or even calculate the trajectory of a basketball shot! Also, a common mistake in solving quadratics is neglecting to check for two solutions after taking the square root. Just remember they can be positive or negative; so if you're not careful, you might miss a critical part of the solution!