Expanding, x² + 2x - 143 = 0.
["# Expanding and Solving the Quadratic Equation: x² + 2x - 143 = 0", "Solving quadratic equations is a fundamental skill in algebra with widespread applications in science, engineering, economics, and everyday problem solving. One common equation students encounter is x² + 2x - 143 = 0. In this article, we explore how to expand, solve, and interpret this quadratic equation using step-by-step methods. Whether you’re a student learning algebra or a teacher seeking clear explanations, this guide will provide valuable insights into expanding and solving quadratic expressions.", "## Understanding the Quadratic Equation: x² + 2x - 143 = 0", "A quadratic equation is any equation of the form:\nax² + bx + c = 0\nwhere a, b, and c are constants and a ≠ 0.\nIn our equation:\n- a = 1\n- b = 2\n- c = -143", "The term x² represents a squared variable, the term 2x is linear, and -143 is the constant. Expanding and solving this involves techniques that apply broadly to quadratics, helping you expand expressions and find real or complex roots.", "---", "## Step 1: Expanding (Factoring), When Applicable", "While the equation x² + 2x - 143 = 0 is already expanded, understanding when and how to "expand" is essential—especially when simplifying or transforming equations. In many cases, factoring a quadratic involves expanding the factors to verify.", "Let’s explore factoring x² + 2x - 143.", "To factor:\nWe need two numbers that multiply to -143 and add to 2 (the coefficient of x).", "Looking at factors of -143:\n- 13 × (-11) = -143, and 13 + (−11) = 2 → This works!", "So, we can factor the quadratic as:\n(x + 13)(x - 11) = 0", "Expanding this verification:\n(x + 13)(x - 11) = x² - 11x + 13x - 143 = x² + 2x - 143 ✓", "While factoring doesn’t technically “expand” in the traditional sense, it demonstrates how expanding binomials recreates the original quadratic—an essential algebra skill.", "---", "## Step 2: Solving by Factoring", "From the factored form:\n(x + 13)(x - 11) = 0", "Use the zero product property: if a product equals zero, then each factor is zero:\n- x + 13 = 0 → x = −13\n- x − 11 = 0 → x = 11", "Solutions: x = −13 and x = 11\nThese are the roots of the equation, showing where the graph intersects the x-axis.", "---", "## Step 3: Using the Quadratic Formula (When Factoring Is Hard)", "Sometimes factoring isn’t straightforward. For x² + 2x - 143 = 0, we can apply the quadratic formula:\n[\nx = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\n]\nPlug in a = 1, b = 2, c = -143:\n[\nx = \frac{-2 \pm \sqrt{(2)^2 - 4(1)(-143)}}{2(1)} = \frac{-2 \pm \sqrt{4 + 572}}{2} = \frac{-2 \pm \sqrt{576}}{2}\n]\nSince √576 = 24,\n[\nx = \frac{-2 \pm 24}{2}\n]\nThus:\n- x = (−2 + 24)/2 = 22/2 = 11\n- x = (−2 − 24)/2 = −26/2 = −13", "Again, we get x = 11 and x = −13.", "---", "## Real-World Applications of the Equation x² + 2x - 143 = 0", "Quadratic equations model real-life scenarios, including:\n- Projectile motion: Calculating the time when a launched object hits the ground\n- Profit optimization: Finding break-even points in business math\n- Engineering design: Determining dimensions for structural components\n- Physics problems: Energy conservation and motion calculations", "Modeling these situations often starts with expanding and solving quadratics like x² + 2x - 143 = 0 to find critical values.", "---", "## Conclusion", "Expanding and solving quadratic equations—such as x² + 2x - 143 = 0—builds foundational algebra skills with lasting practical value. By factoring, applying the quadratic formula, and verifying roots, students gain confidence in handling expressive algebraic models. Whether in math class, standardized tests, or real-world problem solving, mastering quadratics like this opens doors to deeper mathematical understanding.", "Keep practicing: Try expanding other quadratics, factoring more problems, and solving diverse quadratic equations to solidify your algebraic expertise!", "---", "### Related Keywords for SEO:\n- Solve x² + 2x - 143 = 0 step-by-step\n- Expanding quadratic expressions explained\n- How to solve ax² + bx + c = 0\n- Real-world quadratic equations\n- Algebraic problem solving techniques\n- Factor x² + 2x - 143\n- Quadratic solutions using formula and factoring", "By optimizing content with these keywords, your article ranks well for learners seeking clarity on expanding and solving quadratic equations."]
