METHOD 2: SQUAR \( 7 . x^{2}=225 \)

To solve the equation \( 7 \cdot x^{2} = 225 \), the first step is to isolate \( x^{2} \). You can do this by dividing both sides of the equation by 7: \[ x^{2} = \frac{225}{7} \approx 32.14. \] Now, to find \( x \), take the square root of both sides, giving you two possible solutions: \[ x \approx \sqrt{32.14} \approx 5.67 \, \text{and} \, x \approx -5.67. \] Keep in mind that both the positive and negative roots are valid solutions in this context! In many real-world applications, especially in fields like physics and engineering, quadratic equations where the variable is squared arise frequently, whether it's calculating trajectories or optimizing parameters. Understanding how to manipulate these equations is crucial for practical problem-solving in design and analysis, allowing professionals to predict outcomes and make informed decisions effectively!