If \(x^2 - 5x + 6 = 0\), what are the values of \(x\)?

["SEO Article: Solving the Quadratic Equation (x^2 - 5x + 6 = 0) – Find the Values of (x)", "When you're faced with a quadratic equation like (x^2 - 5x + 6 = 0), solving for (x) becomes a straightforward yet essential math skill. Whether you're a student learning algebra basics or a teacher preparing lessons, understanding how to find the roots of quadratic equations is key. In this article, we explore how to solve (x^2 - 5x + 6 = 0) and uncover the values of (x) that satisfy this equation.", "### Understanding the Equation", "The equation (x^2 - 5x + 6 = 0) is a standard quadratic equation in the form (ax^2 + bx + c = 0), where:\n- (a = 1)\n- (b = -5)\n- (c = 6)", "This equation represents a parabola opening upwards (since (a > 0)), and solving it means finding the (x)-coordinates of its points where the curve intersects the (x)-axis (the roots).", "### Factoring the Quadratic", "One of the most efficient ways to solve this equation is by factoring. We seek two numbers that multiply to (c = 6) (the constant term) and add up to (b = -5) (the coefficient of (x)).", "The numbers (-2) and (-3) satisfy these conditions because:\n- ((-2) \ imes (-3) = 6)\n- ((-2) + (-3) = -5)", "So, we rewrite the quadratic equation as:", "[\nx^2 - 5x + 6 = (x - 2)(x - 3) = 0\n]", "### Solving for (x)", "Using the zero product property, if the product of two factors is zero, then at least one of the factors must be zero:", "[\nx - 2 = 0 \quad \ ext{or} \quad x - 3 = 0\n]", "Solving each equation gives:", "[\nx = 2 \quad \ ext{or} \quad x = 3\n]", "### Verifying the Solutions", "You can always double-check by plugging the values back into the original equation:", "- For (x = 2):\n (2^2 - 5(2) + 6 = 4 - 10 + 6 = 0), which is correct.\n- For (x = 3):\n (3^2 - 5(3) + 6 = 9 - 15 + 6 = 0), which is also correct.", "### Why This Equation Matters", "Solving quadratic equations like (x^2 - 5x + 6 = 0) is more than just an academic exercise. These concepts apply in real-world scenarios such as physics (projectile motion), economics (profit models), and engineering (designing structures). Understanding how to factor and solve quadratics forms a foundation for tackling more advanced topics like polynomials, calculus, and differential equations.", "### Final Answer", "The values of (x) that satisfy the equation (x^2 - 5x + 6 = 0) are:", "[\n\boxed{2 \ ext{ and } 3}\n]", "By mastering how to solve quadratic equations, learners gain invaluable problem-solving skills applicable across disciplines. Start practicing factoring, applying the quadratic formula as a backup, and soon you’ll solve any quadratic with confidence!", "---", "Keywords: solve (x^2 - 5x + 6 = 0), quadratic equation solutions, factoring quadratic, roots of (x^2 - 5x + 6), algebra tutorial, quadratic formula, verify solutions, math problem-solving, quadratic equations explained", "For more math help, visit yourmathresources.com — your go-to for clear, accurate algebra tutorials!"]