\[ x = rac{-(-4) \pm \sqrt{64}}{2(2)} \]

["Understanding the Quadratic Formula: Solving ( x = \dfrac{-(-4) \pm \sqrt{64}}{2(2)} )", "When solving quadratic equations, one of the most essential tools is the quadratic formula:", "[\nx = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\n]", "An interesting example that illustrates this formula clearly is:", "[\nx = \frac{-(-4) \pm \sqrt{64}}{2(2)}\n]", "This expression appears in the solution of a quadratic equation derived from the standard form ( ax^2 + bx + c = 0 ). Let’s break it down and explore what this equation represents, how it connects to the quadratic formula, and how to solve it step-by-step—all while optimizing for SEO to help readers understand this important concept.", "---", "### Deriving the Equation from the Quadratic Formula", "The quadratic formula solves equations of the form:\n[\nax^2 + bx + c = 0\n]", "For this example, the numerator (-(-4)) indicates that ( b = 4 ), since (-b = -(-4)). The denominator ( 2(2) ) confirms ( 2a = 2 \ imes 2 = 4 ), so ( a = 2 ).", "Now, plug values into the quadratic formula:", "[\nx = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{-4 \pm \sqrt{(4)^2 - 4(2)(c)}}{2 \ imes 2}\n]", "However, in your given expression, the discriminant is 64, meaning ( b^2 - 4ac = 64 ). Thus, ( \sqrt{64} = 8 ), giving:", "[\nx = \frac{-4 \pm 8}{4}\n]", "This sets the stage for solving two possible solutions, depending on whether we use (+) or (-) in the (\pm) sign.", "---", "### Solving the Equation Step-by-Step", "Start with:\n[\nx = \frac{-(-4) \pm \sqrt{64}}{2(2)} = \frac{4 \pm 8}{4}\n]", "Split into two cases:", "- Positive root:\n[\nx = \frac{4 + 8}{4} = \frac{12}{4} = 3\n]", "- Negative root:\n[\nx = \frac{4 - 8}{4} = \frac{-4}{4} = -1\n]", "Thus, the solutions are ( x = 3 ) and ( x = -1 )—the two roots of the corresponding quadratic equation.", "For full clarity, the equivalent quadratic equation is:", "[\nx^2 + 4x + 16 = 0\n]", "Check by factoring or via the quadratic formula—both confirm the same solutions.", "---", "### Why This Formula Matters in Mathematics", "This form of solving quadratics is foundational across science, engineering, and economics, wherever motion, growth, or optimization is modeled mathematically. Understanding how to:", "- Identify ( a ), ( b ), ( c ) from the formula\n- Simplify square roots and numerators\n- Apply (\pm ) for dual solutions", "…lays the groundwork for more advanced algebra and calculus concepts.", "---", "### SEO Optimization: Key Terms to Rank High", "To maximize visibility for search engines targeting quadratic equations, optimize content around:", "- Quadratic formula explained\n- Solving quadratic equations step-by-step\n- How to find roots using discriminant\n- Example solving ( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} )\n- Applications of the quadratic formula", "These targeted keywords align with user search intent while clearly communicating the topic’s depth.", "---", "### Summary", "The equation\n[\nx = \frac{-(-4) \pm \sqrt{64}}{2(2)}\n]\nis a direct application of the quadratic formula, derived from coefficients extracted from a quadratic expression. By solving it step-by-step, we find the solutions ( x = 3 ) and ( x = -1 ), illustrating how the formula efficiently identifies all possible roots.", "Whether for homework, study, or real-world modeling, mastering this expression strengthens your algebraic fluency and enables tackling complex problems with confidence.", "---", "Next Steps: Practice with other quadratics, explore discriminant analysis, and apply these roots in physics and finance to see the quadratic formula’s power in action!", "---", "Keywords: quadratic formula, solve quadratic equation, discriminant 64, find x solutions, step-by-step quadratic, math tutorial, algebra homework help, discriminant simplifying roots\nMeta title: How to Solve ( x = \frac{-(-4) \pm \sqrt{64}}{4} ) – Step-by-Step Guide\nMeta description: Master quadratic equations with the formula ( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ). Learn step-by-step with example and real-world applications."]