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

["Solving So ( (x + 3)(x - 1) = 8 ): Step-by-Step Explanation & Solutions", "Divide the quadratic mystery in algebra! If you’ve stumbled upon the equation ( (x + 3)(x - 1) = 8 ) while studying quadratics, you’re in the right place. This article breaks down how to solve it clearly, uses logical steps, and explains key algebraic concepts—plus offers practical tips to master solving similar equations.", "---", "### Understanding the Equation: Why ( (x + 3)(x - 1) = 8 )?", "At its core, this equation is a quadratic equation in disguise. It starts as a product of two binomials, shaped by the familiar binomial multiplication pattern:\n[\n(x + 3)(x - 1)\n]\nWhen expanded, this becomes a second-degree polynomial, which we can rearrange into standard quadratic form.", "The right side equals ( 8 ), a constant value—this sets up an equation where the product equals a number, hinting at finding values of ( x ) that satisfy equality.", "---", "### Step 1: Expand the Left Side", "Let’s expand ( (x + 3)(x - 1) ):\n[\n(x + 3)(x - 1) = x^2 - x + 3x - 3 = x^2 + 2x - 3\n]", "So the equation becomes:\n[\nx^2 + 2x - 3 = 8\n]", "---", "### Step 2: Bring All Terms to One Side (Standard Form)", "Subtract 8 from both sides:\n[\nx^2 + 2x - 3 - 8 = 0 \quad \Rightarrow \quad x^2 + 2x - 11 = 0\n]", "Now we have a standard quadratic equation:\n[\nx^2 + 2x - 11 = 0\n]", "---", "### Step 3: Solve the Quadratic Using the Quadratic Formula", "To find ( x ), we use the quadratic formula:\n[\nx = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\n]", "Identify coefficients from ( ax^2 + bx + c = 0 ):\n- ( a = 1 )\n- ( b = 2 )\n- ( c = -11 )", "Plug into the formula:\n[\nx = \frac{-2 \pm \sqrt{(2)^2 - 4(1)(-11)}}{2(1)} = \frac{-2 \pm \sqrt{4 + 44}}{2} = \frac{-2 \pm \sqrt{48}}{2}\n]", "Simplify:\n[\n\sqrt{48} = \sqrt{16 \ imes 3} = 4\sqrt{3}\n]", "So:\n[\nx = \frac{-2 \pm 4\sqrt{3}}{2} = -1 \pm 2\sqrt{3}\n]", "---", "### Final Solutions", "The two real solutions are:\n[\nx = -1 + 2\sqrt{3} \quad \ ext{and} \quad x = -1 - 2\sqrt{3}\n]", "These exact forms capture all valid solutions, but for approximate decimal values:\n[\nx \approx 2.464 \quad \ ext{and} \quad x \approx -4.464\n]", "---", "### Why This Matters: Real-World Applications & Learning Benefits", "Understanding how to solve equations like ( (x + 3)(x - 1) = 8 ) helps in many areas: engineering, physics, economics, and computer modeling—where relationships between variables often form quadratic patterns.", "Mastering expanding, simplifying, and solving quadratics builds confidence in algebra fundamentals and prepares students for advanced math topics.", "---", "### Tips for Solving Similar Equations", "1. Expand the product before rearranging—this turns the problem into standard quadratic form.\n2. Always move constants to one side to form ( ax^2 + bx + c = 0 ).\n3. Use the quadratic formula smartly when factoring isn’t easy.\n4. Check your work by plugging solutions back into the original equation.\n5. Simplify radicals, but leave them in exact form unless requested otherwise.", "---", "### Summary", "Equation ( (x + 3)(x - 1) = 8 ) leads to the solvable quadratic ( x^2 + 2x - 11 = 0 ). Using expansion and the quadratic formula, we find two real solutions:\n[\nx = -1 + 2\sqrt{3}, \quad x = -1 - 2\sqrt{3}\n]\nThese are key entries in solving quadratic equations—essential for mastering algebra and applying it in real contexts.", "---", "Keywords: solve ( (x + 3)(x - 1) = 8 ), quadratic equation solutions, expand and solve, quadratic formula, standard form, algebra basics, real solutions, exact form solutions", "Meta Description:\nLearn how to solve ( (x + 3)(x - 1) = 8 ) step-by-step. Discover expansion, rearranging, and applying the quadratic formula to find exact solutions and boost your algebraic confidence.", "---", "Ready to master quadratic equations? Explore more tutorials on solving polynomials, factoring techniques, and applications in real-world math problems!"]