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

["Title: Solving ( x(x - 1) = 8 ): A Step-by-Step Guide to Quadratic Equations", "---", "### Introduction", "The equation ( x(x - 1) = 8 ) is a simple yet powerful example of transforming a real-world inspired problem into a quadratic equation. Often encountered in algebra, understanding how to solve such equations opens the door to tackling more complex math and applications in science, engineering, and finance.", "In this SEO-optimized article, we’ll explore how to solve ( x(x - 1) = 8 ), explain key algebraic concepts, and highlight why this equation matters. Whether you’re a student, teacher, or self-learner, mastering this problem builds a strong foundation in solving quadratic equations.", "---", "### What Does ( x(x - 1) = 8 ) Represent?", "The expression ( x(x - 1) ) appears in various real-life scenarios, such as modeling the area of irregular shapes or solving optimization problems. In pure mathematics, rewriting it in standard quadratic form helps unlock powerful solving techniques like factoring, completing the square, or using the quadratic formula.", "---", "### Step 1: Expand and Rearrange Into Standard Quadratic Form", "Start by expanding the left-hand side:", "[\nx(x - 1) = x^2 - x\n]", "Now set equal to 8:", "[\nx^2 - x = 8\n]", "Move all terms to one side:", "[\nx^2 - x - 8 = 0\n]", "Now we have a standard quadratic equation:\n[\nx^2 - x - 8 = 0\n]", "---", "### Step 2: Solve the Quadratic Equation", "We can solve this using the quadratic formula:", "[\nx = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\n]", "For ( x^2 - x - 8 = 0 ), the coefficients are:\n( a = 1 ), ( b = -1 ), ( c = -8 )", "Calculate the discriminant:", "[\nb^2 - 4ac = (-1)^2 - 4(1)(-8) = 1 + 32 = 33\n]", "Since the discriminant is positive, there are two distinct real roots.", "Apply the quadratic formula:", "[\nx = \frac{-(-1) \pm \sqrt{33}}{2(1)} = \frac{1 \pm \sqrt{33}}{2}\n]", "---", "### Final Solutions", "Thus, the solutions are:", "[\nx = \frac{1 + \sqrt{33}}{2} \quad \ ext{and} \quad x = \frac{1 - \sqrt{33}}{2}\n]", "---", "### Why This Equation Matters", "Solving ( x(x - 1) = 8 ) is more than just practice with quadratics—it prepares you for:", "- Modeling growth and decay in biology and economics\n- Calculating areas in geometry involving binomial expressions\n- Understanding parabolic behavior in physics and data analysis\n- Strengthening algebraic reasoning for advanced problem-solving", "Moreover, mastering step-by-step equation solving aligns with best SEO practices by using targeted keywords such as “solve ( x(x-1) = 8 )”, “quadratic equation solutions,” and “step-by-step quadratic formula.”", "---", "### Practice & Real-World Applications", "Try solving similar equations:\nCompare\n( x(x - 2) = 15 ) or ( (x+1)(x - 3) = 6 )", "These teach transformations and factoring strategies. Try graphing the function ( y = x(x - 1) ) to visualize where it intersects ( y = 8 )—useful for understanding roots and behavior.", "---", "### Summary", "The equation ( x(x - 1) = 8 ) leads neatly to the quadratic form ( x^2 - x - 8 = 0 ), solvable by the quadratic formula:", "[\nx = \frac{1 \pm \sqrt{33}}{2}\n]", "This process strengthens foundational algebra skills and prepares learners for advanced mathematics and real-world problem solving.", "For those seeking clarity and precision in solving quadratic equations, consistent practice with well-structured problems enhances comprehension and confidence.", "---", "Keywords (SEO meta elements):\nx(x−1)=8, quadratic equation solutions, solve x(x−1)=8, step-by-step quadratic formula, real number solutions, algebra tutorial, quadratic formula practice, solve x²−x−8=0, real-world equations", "Tags: #Algebra #QuadraticEquations #MathTips #SolveQuadratic #HighSchoolMath #STEMLearning", "---", "Stay curious. Keep solving quadratic equations."]