Expand: x² + 2x − 3 = 8 → x² + 2x − 11 = 0.

["Title: Expanding and Solving: How to Transform and Solve the Quadratic Equation x² + 2x − 3 = 8", "Solving quadratic equations is a fundamental skill in algebra, essential for students, educators, and DIY math enthusiasts. One common task involves expanding and simplifying an equation before applying standard solving techniques. In this article, we explore how to transform the equation x² + 2x − 3 = 8 into a standard quadratic form—x² + 2x − 11 = 0—and walk through the step-by-step process for solving it. Understanding this method unlocks powerful problem-solving techniques in algebra and beyond.", "---", "### Step 1: Rewriting the Equation", "The original equation is:\n$$x^2 + 2x - 3 = 8$$", "To convert it into the standard quadratic form ax² + bx + c = 0, we subtract 8 from both sides:\n$$x^2 + 2x - 3 - 8 = 0$$", "Simplifying the constants:\n$$x^2 + 2x - 11 = 0$$", "Now, the equation is in the classic quadratic format—ready for solving using factoring, completing the square, or the quadratic formula.", "---", "### Step 2: Solving the Quadratic Equation", "With the equation\n$$x^2 + 2x - 11 = 0$$\nwe can apply the quadratic formula:\n$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$\nwhere (a = 1), (b = 2), and (c = -11).", "Calculate the discriminant:\n$$b^2 - 4ac = 2^2 - 4(1)(-11) = 4 + 44 = 48$$", "Since the discriminant is positive, there are two real, distinct solutions:\n$$x = \frac{-2 \pm \sqrt{48}}{2} = \frac{-2 \pm 4\sqrt{3}}{2} = -1 \pm 2\sqrt{3}$$", "Thus, the solutions are:\n$$x = -1 + 2\sqrt{3} \quad \ ext{and} \quad x = -1 - 2\sqrt{3}$$", "---", "### Step 3: Practical Applications and Expanded Learning", "Working with equations like x² + 2x − 3 = 8 teaches critical algebraic manipulation skills:", "- Isolating terms: Understanding how to move constants across the equals sign.\n- Simplifying expressions: Combining like terms to form a standard form.\n- Applying powerful formula use: Mastery of the quadratic formula accelerates solving.", "These skills apply in physics, engineering, economics, and computer science—fields where modeling real-world phenomena relies on solving nonlinear equations.", "---", "### Step 4: Graphical Interpretation", "The quadratic equation x² + 2x - 11 = 0 represents a parabola. Its graph crosses the x-axis at the roots x = -1 ± 2√3, visualizing where y = x² + 2x − 3 equals 8. Graphing tools or hand-drawn sketches give real insight into the equation’s behavior and solutions.", "---", "### Summary", "Expanding and simplifying equations is more than just algebra—it’s the first step toward insight and solution. Transforming\n$$x^2 + 2x - 3 = 8\n$$\ninto\n$$x^2 + 2x - 11 = 0\n$$\nenables efficient use of standard solving methods. Whether you’re tackling homework, preparing for exams, or exploring advanced math, mastering these steps empowers you to navigate quadratic challenges confidently.", "---", "### Further Reading", "- How to Factor Quadratic Equations\n- Using the Quadratic Formula in Real Life\n- Graphing Quadratics and Analyzing Parabolas", "Whether you're a student, teacher, or lifelong learner, sharpening your quadratic-solving skills starts with this simple yet powerful transformation.", "---", "Keywords for SEO:\nquadratic equation, how to solve x² + 2x − 3 = 8, expand x² + 2x − 3 = 8, shift quadratic equation, quadratic formula, solve x² + 2x − 11 = 0, algebra help, quadratic roots, simplifying quadratics, real-world math applications.\nMeta Description:\nLearn how to expand and solve quadratic equations with step-by-step instructions. Transform x² + 2x − 3 = 8 into x² + 2x − 11 = 0, then solve using the quadratic formula. Master essential algebra skills today."]