![Solution: Group and complete the square: $ 4(x^2 + 2x) - 9(y^2 - 2y) = 11 $. Complete squares: $ 4[(x+1)^2 - 1] - 9[(y-1)^2 - 1] = 11 $. Expand: $ 4(x+1)^2 - 4 - 9(y-1)^2 + 9 = 11 \Rightarrow 4(x+1)^2 - 9(y-1)^2 = 6 $. Rewrite: $ \frac{(x+1)^2}{\frac{3}{2}} - \frac{(y-1)^2}{\frac{2}{3}} = 1 $. Center at $ (-1, 1) $. \boxed{(-1, 1)}1. **A chemistry experiment requires 50 mL of a 10% salt solution. If you only have a 20% salt solution and distilled water, how much of each should be mixed to obtain](https://soloferat.biz.id/images/solution-group-and-complete-the-square-4x2-2x-9y2-2y-11-complete-squares-4x12-1-9y-12-1-11-expand-4x12-4-9y-12-9-11-rightarrow-4x12-9y-12-6-rewrite-fracx12frac32-fracy-1.jpg)
["Understanding the Equation: 0.20x = 0.10 × 50
\nA Simple Guide to Solving Linear Equations", "When encountering mathematical expressions like 0.20x = 0.10 × 50, it’s common to pause and analyze how these equations work. Whether you're a student, teacher, or someone learning algebra, breaking this equation down helps strengthen foundational math skills—especially useful when solving for x. This article explains the step-by-step process of solving 0.20x = 0.10 × 50, why it’s important, and how mastering these steps supports broader math learning.", "---", "### What Does the Equation Mean?", "Start by interpreting the equation:", "> 0.20x = 0.10 × 50", "On the right side, 0.10 × 50 is multiplication.
\nCalculating this gives:
\n0.10 × 50 = 5", "So the equation simplifies to:
\n0.20x = 5", "This tells us that 20% of x equals 5. Solving for x means finding the full value of x that produces this result.", "---", "### How to Solve for x", "To isolate x, divide both sides of the equation by 0.20:", "$$
\nx = \frac{5}{0.20}
\n$$", "Now compute the division:", "$$
\nx = \frac{5}{0.20} = \frac{5}{1/5} = 5 \ imes 5 = 25
\n$$", "✅ Solution: x = 25", "---", "### Why Knowing How to Solve Such Equations Matters", "Understanding how to isolate variables like x using multiplication, division, and basic algebra forms the backbone of solving more complex equations—critical in chemistry, physics, engineering, and data analysis. The equation 0.20x = 0.10 × 50 may seem simple, but it reinforces key concepts:", "- Multiplication and division are inverse operations.
\n- Equations maintain balance. What you do to one side, you must do to the other.
\n- Simplifying expressions helps clarify like terms.
\n- Restaking both sides by decimals or fractions clears ambiguity.", "Mastering these patterns builds confidence and accuracy in math—essential when tackling real-world problems such as budgeting, scaling formulas in science, or analyzing growth trends.", "---", "### Practical Example: Applying the Solution", "Suppose x represents the cost of an item after a 20% discount, and 0.10 × 50 represents a selling price split into parts. Understanding x = 25 clarifies how much was discounted or how pricing breaks down—useful for both math and everyday reasoning.", "---", "### Summary: Key Takeaways", "- 0.20x = 0.10 × 50 simplifies to 0.20x = 5
\n- Solving for x involves dividing both sides by 0.20
\n- The solution is x = 25
\n- This basic equation reinforces core algebra principles
\n- Strong algebra skills enable solving complex problems across sciences and math", "---", "### Practice Tips", "- Try converting decimals to fractions to avoid rounding errors.
\n- Try similar equations with different decimals: 0.75x = 0.25 × 20
\n- Apply algebra to real-life scenarios like unit pricing or interest calculations.", "---", "Mastering equations like 0.20x = 0.10 × 50 helps unlock advanced math and builds logical thinking essential for studying STEM disciplines. Keep practicing—it’s the foundation that opens doors to deeper learning in science, finance, and beyond.", "---", "Keywords: algebra, solving equations, linear equations, decimals, math tips, equation solving, x value, math fundamentals, solving 0.20x, 0.10 × 50, decimals and fractions, math problem solving."]
