Usando la fórmula cuadrática W = (-b ± √(b² - 4ac)) / 2a, donde a = 4, b = 48 y c = -171, obtenemos W = (-48 ± √(48² - 4*4*(-171))) / 8.
["How to Use the Quadratic Formula to Solve Equations: A Step-by-Step Guide with Examples", "Solving quadratic equations is a fundamental skill in algebra, essential for students, mathematicians, and professionals alike. One of the most powerful tools available is the quadratic formula, which provides an exact solution for any quadratic equation in the form W = ax² + bx + c = 0.", "In this article, we’ll explore the standard quadratic formula:\nW = (−b ± √(b² − 4ac)) / (2a)", "We’ll break down how to use this formula step-by-step, focusing on a specific example:\nUsing ( a = 4 ), ( b = 48 ), and ( c = -171 ) to find W.", "---", "### What Is the Quadratic Formula?", "The quadratic formula solves equations of the form:\nax² + bx + c = 0, where a ≠ 0.\nIt helps find the values of x (often interpreted as the roots or zeros of the quadratic function) efficiently, even when factoring is difficult or impossible.", "---", "### Step-by-Step: Applying the Formula", "Let’s apply the formula to the values given:\n- ( a = 4 )\n- ( b = 48 )\n- ( c = -171 )", "#### 1. Plug values into the formula:\n[\nW = \frac{ -b \pm \sqrt{b^2 - 4ac} }{ 2a }\n]\n[\nW = \frac{ -48 \pm \sqrt{48^2 - 4 \cdot 4 \cdot (-171)} }{ 2 \cdot 4 }\n]", "#### 2. Calculate the discriminant (( \Delta = b^2 - 4ac )):\n[\n\Delta = 48^2 - 4 \cdot 4 \cdot (-171) = 2304 + 2736 = 5040\n]", "#### 3. Plug the discriminant back in:\n[\nW = \frac{ -48 \pm \sqrt{5040} }{ 8 }\n]", "#### 4. Simplify √5040 (optional, for exact values):\nFactor 5040:\n5040 = 16 × 315 = 16 × 9 × 35 = ( 16 \ imes 9 \ imes (5 \ imes 7) )\n[\n\sqrt{5040} = \sqrt{16 \cdot 9 \cdot 5 \cdot 7} = 4 \cdot 3 \cdot \sqrt{35} = 12\sqrt{35}\n]", "So the solutions become:\n[\nW = \frac{ -48 \pm 12\sqrt{35} }{ 8 }\n]", "#### 5. Simplify the expression:\nDivide numerator and denominator by 4:\n[\nW = \frac{ -12 \pm 3\sqrt{35} }{ 2 }\n]", "This gives two exact solutions:\n[\nW_1 = \frac{ -12 + 3\sqrt{35} }{ 2 }, \quad W_2 = \frac{ -12 - 3\sqrt{35} }{ 2 }\n]", "---", "### Why Use the Quadratic Formula?", "- Always works: Unlike factoring, it finds roots even for non-factorable quadratics.\n- Clear structure: Uses precise, standardized calculations.\n- Foundational for advanced math: Key in calculus, engineering, and physics.\n- Efficient for computation: Fast with modern calculators and software.", "---", "### Real-World Applications", "Quadratic equations model parabolic paths in physics, optimize profits in economics, and guide structural design in engineering. Solving them accurately ensures reliable predictions and solutions.", "---", "### Conclusion", "The quadratic formula, W = (−b ± √(b² − 4ac)) / (2a), is an essential algebraic tool. Applying it step-by-step—identifying a, b, and c, computing the discriminant, and simplifying—yields exact solutions even with complex numbers. Whether you're a student mastering algebra or a professional solving real-world problems, mastering this formula unlocks deeper mathematical insight and precision.", "---", "### Want to Solve It Yourself?", "Try plugging in your own a, b, and c values into the formula:\n[\nW = \frac{ -b \pm \sqrt{b^2 - 4ac} }{ 2a }\n]\nAnd remember: a positive discriminant yields two real solutions, zero means one real root, and a negative discriminant gives complex solutions.", "---", "Keywords for SEO: Quadratic Formula, Solve Quadratic Equation, W = (-b ± √(b² - 4ac)) / 2a, Algebra Tutorial, Quadratic Solutions, Find Roots of Quadratics, Mathematics Guide", "Meta Description:\nLearn how to use the quadratic formula ( W = \frac{ -b \pm \sqrt{b^2 - 4ac} }{ 2a } ) with step-by-step examples, including discriminant calculation, exact solutions, and real-world applications. Ideal for students and math learners.", "---", "Master the quadratic formula today — every equation becomes solvable!"]
