\frac{25}{16}x^2 = 25

["# How to Solve (\frac{25}{16}x^2 = 25): A Comprehensive Step-by-Step Guide", "Understanding how to solve equations like (\frac{25}{16}x^2 = 25) is essential for mastering algebra and solving real-world problems. Whether you're a high school student or a self-learner, knowing how to isolate variables and manipulate fractions and exponents can significantly boost your math proficiency.", "## Understanding the Equation", "The equation you're given is:", "[\n\frac{25}{16}x^2 = 25\n]", "This is a quadratic equation involving a squared term. Our goal is to solve for (x), the variable we want to isolate.", "## Step-by-Step Solution", "### Step 1: Eliminate the fraction by multiplying both sides by 16", "To eliminate the denominator (\frac{16}{16}), multiply every term in the equation by 16:", "[\n16 \cdot \frac{25}{16}x^2 = 16 \cdot 25\n]", "Simplifying both sides gives:", "[\n25x^2 = 400\n]", "---", "### Step 2: Isolate (x^2) by dividing both sides by 25", "To isolate (x^2), divide both sides of the equation by 25:", "[\nx^2 = \frac{400}{25}\n]", "[\nx^2 = 16\n]", "---", "### Step 3: Solve for (x) by taking the square root", "Now take the square root of both sides:", "[\nx = \pm\sqrt{16}\n]", "[\nx = \pm 4\n]", "---", "## Final Answer", "[\n\boxed{x = 4 \quad \ ext{or} \quad x = -4}\n]", "## Why This Matters", "This equation demonstrates the fundamental algebra skills needed to solve quadratic equations, including handling fractions, isolating variables, and applying square roots. Mastering such problems helps build a strong foundation for more advanced topics like calculus, physics equations, and engineering applications.", "## Related Keywords for SEO Optimization", "- Solve quadratic equation steps\n- Algebra equation solutions for x\n- How to solve (\frac{25}{16}x^2 = 25)\n- Step-by-step quadratic equation tutorial\n- 25 over 16 times x squared equals 25\n- Quadratic equations with fractions explained\n- Solve (x^2 = 16)\n- Algebra2 lesson: solving for x in quadratic form", "---", "By breaking down the equation calmly and clearly, anyone can confidently solve (\frac{25}{16}x^2 = 25) and apply these skills across more complex areas of math. If you found this guide helpful, share it with fellow learners — mastering algebra starts with understanding the basics!"]