x = rac{-2 \pm \sqrt{4 + 24}}{2} = rac{-2 \pm \sqrt{28}}{2} = rac{-2 \pm 2\sqrt{7}}{2} = -1 \pm \sqrt{7}

["Understanding the Quadratic Formula: Simplifying x = (−2 ± √(4 + 24)) / 2", "When solving quadratic equations, one of the most powerful tools at your disposal is the quadratic formula. For an equation in the standard form ( ax^2 + bx + c = 0 ), the solutions are given by:", "[\nx = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\n]", "In this article, we’ll break down the process and simplify the expression:", "[\nx = \frac{-2 \pm \sqrt{4 + 24}}{2}\n]", "---", "### Step-by-Step Simplification", "Start with the original expression:", "[\nx = \frac{-2 \pm \sqrt{4 + 24}}{2}\n]", "Evaluate the discriminant:\nThe radicand inside the square root is ( b^2 - 4ac = 4 + 24 = 28 ).\nSo we rewrite:", "[\nx = \frac{-2 \pm \sqrt{28}}{2}\n]", "Simplify the square root:\nNote that ( \sqrt{28} = \sqrt{4 \cdot 7} = \sqrt{4} \cdot \sqrt{7} = 2\sqrt{7} ).\nSubstitute this in:", "[\nx = \frac{-2 \pm 2\sqrt{7}}{2}\n]", "Factor and simplify:\nFactor 2 from the numerator:", "[\nx = \frac{2(-1 \pm \sqrt{7})}{2}\n]", "Cancel the common factor of 2:", "[\nx = -1 \pm \sqrt{7}\n]", "---", "### Final Result", "[\nx = -1 \pm \sqrt{7}\n]", "---", "### Why This Simplification Matters", "Simplifying expressions using the quadratic formula not only makes the solution clearer but also easier to work with in further calculations, graphing, or real-world applications. The simplified form ( x = -1 \pm \sqrt{7} ) reveals the two exact solutions:", "- ( x = -1 + \sqrt{7} )\n- ( x = -1 - \sqrt{7} )", "These represent the roots of the original quadratic equation, useful in algebra, physics, engineering, and many optimization problems.", "---", "### Summary", "- Begin with the general quadratic formula and substitute coefficients.\n- Simplify the discriminant carefully.\n- Factor and reduce the expression.\n- Simplified solutions often offer deeper insight and easier use.", "Understanding and mastering this simplification step helps strengthen your problem-solving skills and confidence in working with quadratic equations.", "---", "Keywords: quadratic formula, solve x, simplify radical, x = -1 ± √7, discriminant, algebra, quadratic equations, math tutorial, solving quadratics."]