So \( (x+3)(x-1) = 2^3 = 8 \)

["### Solving So ( (x+3)(x-1) = 8 ): A Step-by-Step Guide", "When faced with the equation ( (x + 3)(x - 1) = 8 ), solving for ( x ) might seem tricky at first, but with a clear, structured approach, it becomes manageable. This article walks you through solving quadratic equations using simple algebra, specifically our example:", "So ( (x + 3)(x - 1) = 2^3 = 8 )", "---", "## Why This Equation Matters", "Quadratic equations like this arise in algebra, physics, economics, and many real-world applications. Simplifying expressions such as ( (x + 3)(x - 1) ) and equating them to constants helps develop strong problem-solving skills and prepares you for more advanced math topics.", "---", "## Step 1: Expand the Left Side", "Begin by expanding the product on the left:", "[\n(x + 3)(x - 1) = x \cdot x + x \cdot (-1) + 3 \cdot x + 3 \cdot (-1)\n= x^2 - x + 3x - 3\n= x^2 + 2x - 3\n]", "Now rewrite the equation:", "[\nx^2 + 2x - 3 = 8\n]", "---", "## Step 2: Move All Terms to One Side", "To form a standard quadratic equation, move 8 to the left side:", "[\nx^2 + 2x - 3 - 8 = 0\n\quad\Rightarrow\quad\nx^2 + 2x - 11 = 0\n]", "Now you have a simple quadratic equation:\n[\nx^2 + 2x - 11 = 0\n]", "---", "## Step 3: Solve Using the Quadratic Formula or Factoring", "This equation doesn’t factor neatly, so using the quadratic formula is reliable:", "[\nx = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\n]", "From ( x^2 + 2x - 11 ), identify:\n( a = 1 ), ( b = 2 ), ( c = -11 )", "Compute the discriminant:\n[\nb^2 - 4ac = (2)^2 - 4(1)(-11) = 4 + 44 = 48\n]", "Now plug into the formula:", "[\nx = \frac{-2 \pm \sqrt{48}}{2}\n]", "Simplify ( \sqrt{48} ):\n[\n\sqrt{48} = \sqrt{16 \cdot 3} = 4\sqrt{3}\n]", "So:", "[\nx = \frac{-2 \pm 4\sqrt{3}}{2} = -1 \pm 2\sqrt{3}\n]", "---", "## Step 4: The Final Answer", "The two solutions are:", "[\nx = -1 + 2\sqrt{3} \quad \ ext{and} \quad x = -1 - 2\sqrt{3}\n]", "These exact solutions are valuable in algebra and calculus, especially when analyzing quadratic functions or graphs.", "---", "## Bonus Tips", "- Check your work: Plug ( x = -1 \pm 2\sqrt{3} ) back into the original equation to verify.\n- Graphing insight: The quadratic ( y = x^2 + 2x - 11 ) is a parabola opening upward with vertex at ( x = -1 ); crossing y=0 at ( x = -1 \pm 2\sqrt{3} ).\n- Real-world use: This method applies to problems involving area, motion, or optimization involving quadratic relationships.", "---", "### Conclusion", "Solving ( (x + 3)(x - 1) = 8 ) leads to a familiar quadratic form, beautifully simplified using algebra. Mastering such steps strengthens your mathematical foundation and opens doors to more complex problem solving.", "---", "Keywords: Solve (x+3)(x-1) = 8, quadratic equation solving, algebra tutorial, expand and solve, using the quadratic formula, exact solutions, simplify (x+3)(x-1), real-world math applications."]