1,500 + 100x + 60x + 4x² = 1,980

["Solving the Quadratic Equation: 1,500 + 100x + 60x + 4x² = 1,980", "When faced with a quadratic equation like 1,500 + 100x + 60x + 4x² = 1,980, simplifying and solving it step by step is key—especially when the coefficients are large, making it easy to lose track. In this article, we’ll break down how to rewrite, simplify, and solve this equation efficiently, showing how mathematical clarity unlocks accurate solutions.", "---", "### Step 1: Combine Like Terms", "The equation is:\n1,500 + 100x + 60x + 4x² = 1,980", "Start by combining the linear terms (terms with x):\n100x + 60x = 160x", "So the equation becomes:\n4x² + 160x + 1,500 = 1,980", "---", "### Step 2: Move All Terms to One Side", "Subtract 1,980 from both sides to set the equation to zero:\n4x² + 160x + 1,500 - 1,980 = 0", "Simplify the constants:\n1,500 - 1,980 = -480", "Now the equation is:\n4x² + 160x - 480 = 0", "---", "### Step 3: Simplify the Quadratic Equation", "All coefficients are divisible by 4, so divide every term by 4:\nx² + 40x - 120 = 0", "This simplified form makes it much easier to apply standard solving techniques, such as factoring, completing the square, or using the quadratic formula.", "---", "### Step 4: Apply the Quadratic Formula", "For equation x² + 40x - 120 = 0, use the quadratic formula:\n[\nx = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\n]", "Here, a = 1, b = 40, and c = -120. Substitute these values:", "- Calculate the discriminant:\n [\n b^2 - 4ac = 40^2 - 4(1)(-120) = 1,600 + 480 = 2,080\n ]", "- Take the square root:\n [\n \sqrt{2,080} = \sqrt{16 \ imes 130} = 4\sqrt{130}\n ]", "- Plug into the formula:\n [\n x = \frac{-40 \pm 4\sqrt{130}}{2} = -20 \pm 2\sqrt{130}\n ]", "---", "### Final Answer", "The solutions to the equation 1,500 + 100x + 60x + 4x² = 1,980 are:\nx = –20 + 2√130\nand\nx = –20 – 2√130", "---", "### Why This Process Matters", "- Clarity through simplification: Combining like terms keeps the equation manageable.\n- Standardization: Dividing by common factors reduces computational errors.\n- Clear solution path: Using the quadratic formula ensures accurate results even with large coefficients.", "For students, teachers, and self-learners alike, mastering these steps transforms complex equations into solvable problems. With practice, identifying like terms and simplifying quadratics becomes second nature—empowering confident problem-solving.", "---", "### Related Searches (SEO Keywords)\n- How to solve 4x² + 160x - 480 = 0\n- Quadratic equation simplified step by step\n- Solve quadratic with large coefficients\n- Quadratic formula example with constants\n- Solve 1,500 + 100x + 60x + 4x² = 1,980", "Start simplifying today—math becomes clearer when you break it down!"]