Solve the quadratic equation \(2x^2 - 4x - 6 = 0\) using the quadratic formula.
["# Solve the Quadratic Equation (2x^2 - 4x - 6 = 0) Using the Quadratic Formula", "Solving quadratic equations is a fundamental skill in algebra, and when traditional factoring proves difficult, the quadratic formula offers a reliable solution. This article explains how to solve the equation (2x^2 - 4x - 6 = 0) using the quadratic formula, step by step.", "---", "## What Is the Quadratic Equation?", "A quadratic equation has the standard form:\n[ ax^2 + bx + c = 0 ]\nwhere (a), (b), and (c) are constants, and (a <br/>\neq 0). The solutions are given by the quadratic formula:\n[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]", "This formula works for any quadratic equation, even when factoring is not straightforward.", "---", "## Step-by-Step: Solving (2x^2 - 4x - 6 = 0)", "### Step 1: Identify coefficients\nFor the equation (2x^2 - 4x - 6 = 0), compare with (ax^2 + bx + c = 0):\n- (a = 2)\n- (b = -4)\n- (c = -6)", "### Step 2: Compute the Discriminant\nThe discriminant (D) determines the nature of the roots:\n[ D = b^2 - 4ac ]\nSubstitute values:\n[ D = (-4)^2 - 4(2)(-6) = 16 + 48 = 64 ]", "Since (D = 64 > 0), there are two distinct real solutions.", "### Step 3: Apply the Quadratic Formula\nNow substitute (a), (b), and (D) into the formula:\n[ x = \frac{-(-4) \pm \sqrt{64}}{2(2)} ]\n[ x = \frac{4 \pm 8}{4} ]", "### Step 4: Solve for Both Roots\nCalculate the two possible values:\n1. ( x = \frac{4 + 8}{4} = \frac{12}{4} = 3 )\n2. ( x = \frac{4 - 8}{4} = \frac{-4}{4} = -1 )", "---", "## Final Answer", "The solutions to the equation (2x^2 - 4x - 6 = 0) are:\n[\nx = 3 \quad \ ext{and} \quad x = -1\n]\nThese values satisfy the original quadratic equation.", "---", "## Why Use the Quadratic Formula?", "When quadratic equations involve large coefficients, messy factoring, or no obvious roots, the quadratic formula provides a quick and accurate method. It applies universally and ensures correct solutions when verified.", "---", "## Summary", "To solve (2x^2 - 4x - 6 = 0):\n1. Identify (a = 2), (b = -4), (c = -6)\n2. Compute discriminant (D = 64)\n3. Apply formula (x = \frac{-b \pm \sqrt{D}}{2a})\n4. Obtain solutions (x = 3) and (x = -1)", "Mastering the quadratic formula empowers you to tackle any quadratic equation with confidence!", "---", "Keywords: quadratic equation, solve (2x^2 - 4x - 6 = 0), quadratic formula, step-by-step solution, discriminant, real roots, algebra tutorial.", "If you’re struggling with quadratic equations, practice using this method—it’s effective and easy once mastered!"]
