Expand and simplify: \(150 + 30x + 20x + 4x^2 = 286\).

["Title: How to Expand and Simplify the Equation (150 + 30x + 20x + 4x^2 = 286) – Step-by-Step Guide", "---", "Table of Contents\n1. Introduction\n2. Expanding the Equation\n3. Simplifying the Expression\n4. Solving for (x)\n5. Verifying the Solution\n6. Tips for Solving Quadratic Equations", "---", "## Introduction", "Solving equations like (150 + 30x + 20x + 4x^2 = 286) is a common task in algebra. This equation combines linear and quadratic terms, forming a quadratic equation that can be simplified and solved using standard methods. Whether you're preparing for exams, handling homework, or working professionally in STEM fields, understanding how to expand and simplify such expressions is crucial.", "In this article, we walk you through each step to expand and simplify the equation (150 + 30x + 20x + 4x^2 = 286), solve for (x), and verify your answer—all while emphasizing SEO-friendly keywords for better online visibility.", "---", "## Expanding the Equation", "Start by observing the left-hand side of the equation:", "[\n150 + 30x + 20x + 4x^2\n]", "Combine like terms—specifically, the linear terms (30x) and (20x):", "[\n(30x + 20x) + 4x^2 + 150 = 4x^2 + 50x + 150\n]", "Thus, the expanded form is:", "[\n4x^2 + 50x + 150 = 286\n]", "SEO keyword: expand quadratic equation", "---", "## Simplifying the Expression", "Now subtract 286 from both sides to set the equation to zero:", "[\n4x^2 + 50x + 150 - 286 = 0 \quad \Rightarrow \quad 4x^2 + 50x - 136 = 0\n]", "This is the simplified standard quadratic form:", "[\n4x^2 + 50x - 136 = 0\n]", "SEO keyword: simplify quadratic equation, standard form quadratic", "---", "## Solving for (x)", "To solve (4x^2 + 50x - 136 = 0), use the quadratic formula:", "[\nx = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\n]", "Here, (a = 4), (b = 50), and (c = -136). Plug in these values:", "[\nx = \frac{-50 \pm \sqrt{50^2 - 4 \cdot 4 \cdot (-136)}}{2 \cdot 4}\n]", "Calculate discriminant:", "[\n50^2 = 2500,\quad 4 \cdot 4 \cdot 136 = 2176,\quad \ ext{so } 2500 + 2176 = 4676\n]", "[\nx = \frac{-50 \pm \sqrt{4676}}{8}\n]", "Approximate (\sqrt{4676} \approx 68.38):", "[\nx \approx \frac{-50 \pm 68.38}{8}\n]", "Now calculate both roots:", "1.\n[\nx_1 = \frac{-50 + 68.38}{8} = \frac{18.38}{8} \approx 2.2975\n]", "2.\n[\nx_2 = \frac{-50 - 68.38}{8} = \frac{-118.38}{8} \approx -14.7975\n]", "SEO keyword: solve quadratic equation, quadratic formula, quadratic roots", "---", "## Verifying the Solution", "It’s important to verify your solutions by plugging them back into the original equation:", "For (x \approx 2.2975):\n[\n4(2.2975)^2 + 50(2.2975) + 150 \approx 21.2 + 114.875 + 150 = 286.075 \approx 286\n]", "For (x \approx -14.7975):\n[\n4(-14.7975)^2 + 50(-14.7975) + 150 \approx 878 - 739.875 + 150 = 288.125 \approx 286 \quad (\ ext{close, small approximations})\n]", "Close results confirm the accuracy due to rounding.", "SEO keyword: verify quadratic solution, check quadratic equation result", "---", "## Tips for Solving Quadratic Equations", "- Always simplify expressions before solving.\n- Combine like terms early to reduce complexity.\n- Use the quadratic formula when factoring is difficult.\n- Calculate discriminant beforehand to check root nature (real/complex).\n- Use a calculator for square roots to improve precision.", "---", "## Conclusion", "Expanding and simplifying (150 + 30x + 20x + 4x^2 = 286) reduces it to (4x^2 + 50x - 136 = 0), a standard quadratic equation easily solved using the quadratic formula. This method ensures accuracy and clarity in solving real-world modeling problems, equations from physics, and optimization scenarios.", "Mastering step-by-step expansion and simplification builds a strong foundation for advanced math and technical fields—perfect for students, educators, and professionals alike.", "Keywords: expand and simplify quadratic equation, solve (4x^2 + 50x - 136 = 0), quadratic formula applications, algebra problem solving, simplify algebraic expressions", "---", "Ready to expand and simplify more equations? Start with combining terms, simplify to standard form, and apply the quadratic formula—easy and effective!", "---", "Meta Description: Learn how to expand and simplify (150 + 30x + 20x + 4x^2 = 286) step-by-step, solve the resulting quadratic equation (4x^2 + 50x - 136 = 0) using the quadratic formula, and verify solutions effectively. SEO keywords: expand quadratic equation, simplify quadratic, quadratic roots formula."]