x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4 \times 1 \times (-8)}}{2 \times 1}

["Solving Quadratic Equations: A Step-by-Step Guide Using the Quadratic Formula", "When faced with a quadratic equation of the form ( ax^2 + bx + c = 0 ), solving for ( x ) becomes straightforward using the powerful quadratic formula:", "[\nx = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\n]", "This method is reliable, efficient, and widely applicable across algebra and higher-level math. In this article, we’ll walk through one specific example:", "[\nx = \frac{-(-4) \pm \sqrt{(-4)^2 - 4 \ imes 1 \ imes (-8)}}{2 \ imes 1}\n]", "---", "### Step 1: Identify Coefficients\nFrom the given equation, match coefficients to ( ax^2 + bx + c = 0 ):\n- ( a = 1 )\n- ( b = -4 )\n- ( c = -8 )", "---", "### Step 2: Plug Into the Quadratic Formula\nSubstitute ( a ), ( b ), and ( c ) into the formula:", "[\nx = \frac{-(-4) \pm \sqrt{(-4)^2 - 4 \ imes 1 \ imes (-8)}}{2 \ imes 1}\n]", "Simplify each term:\n- ( -(-4) = +4 )\n- ( (-4)^2 = 16 )\n- ( 4 \ imes 1 \ imes (-8) = -32 ), so ( -(-32) = +32 )", "The discriminant becomes:\n[\n16 + 32 = 48\n]", "Thus, the equation now looks like:", "[\nx = \frac{4 \pm \sqrt{48}}{2}\n]", "---", "### Step 3: Simplify the Square Root\nFactor ( \sqrt{48} ) to simplify:\n[\n\sqrt{48} = \sqrt{16 \ imes 3} = \sqrt{16} \ imes \sqrt{3} = 4\sqrt{3}\n]", "Now rewrite the solution:\n[\nx = \frac{4 \pm 4\sqrt{3}}{2}\n]", "---", "### Step 4: Final Simplification\nDivide numerator by 2:\n[\nx = 2 \pm 2\sqrt{3}\n]", "Thus, the two solutions are:\n[\nx = 2 + 2\sqrt{3} \quad \ ext{and} \quad x = 2 - 2\sqrt{3}\n]", "---", "### Why Use the Quadratic Formula?\nThe quadratic formula eliminates the need for factoring, especially useful when equations don’t factor neatly. It provides exact solutions and helps analyze the nature of roots (real or complex), repeated, or distinct.", "Whether solving for roots in algebra class or tackling advanced math problems, mastering this formula equips you with a versatile tool for quadratic equations.", "---", "Keywords: quadratic formula, solving quadratic equations, algebra 2, quadratic formula step-by-step, ( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ), discriminant, exact solutions, math problem-solving", "Meta Description:\nLearn how to solve ( x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4 \ imes 1 \ imes (-8)}}{2 \ imes 1} ) using the quadratic formula step-by-step, including simplifying square roots and final simplified solutions. Perfect for students and algebra learners.", "---", "Further Reading:\n- Understanding the Discriminant in Quadratic Equations\n- Applications of the Quadratic Formula in Physics and Engineering\n- Step-by-Step Guide to Completing the Square", "---", "Keep mastering quadratic equations—your math foundation grows stronger with practice!"]