\[600 + 60x + 40x + 4x^2 = 792\]

["Solving the Quadratic Equation: 600 + 60x + 40x + 4x² = 792", "When studying algebra, quadratic equations often appear as key challenges. One such equation is:", "[ 600 + 60x + 40x + 4x^2 = 792 ]", "This article guides you through simplifying, solving, and understanding this quadratic equation step-by-step — making it easier to find solutions and strengthen your algebra skills.", "---", "### Step 1: Simplify the Equation", "Start by combining like terms on the left-hand side:", "[\n600 + 60x + 40x + 4x^2\n]", "Combine the linear terms (60x + 40x = 100x), so the equation becomes:", "[\n4x^2 + 100x + 600 = 792\n]", "Now, move all terms to one side to form a standard quadratic equation:", "[\n4x^2 + 100x + 600 - 792 = 0\n]", "[\n4x^2 + 100x - 192 = 0\n]", "---", "### Step 2: Simplify Further (Optional)", "Quadratic equations are easier to solve when coefficients are small and the equation is simplified. Divide every term by 4 to reduce complexity:", "[\nx^2 + 25x - 48 = 0\n]", "Now the equation is:", "[\nx^2 + 25x - 48 = 0\n]", "---", "### Step 3: Solve the Quadratic Equation", "Since simplifying did not yield factorable integers, we apply the quadratic formula:", "[\nx = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\n]", "From (x^2 + 25x - 48 = 0):\n(a = 1), (b = 25), (c = -48)", "Compute the discriminant:", "[\n\Delta = b^2 - 4ac = 25^2 - 4(1)(-48) = 625 + 192 = 817\n]", "Since the discriminant is positive, there are two real solutions:", "[\nx = \frac{-25 \pm \sqrt{817}}{2}\n]", "---", "### Step 4: Final Answer", "The solutions to the equation (600 + 60x + 40x + 4x^2 = 792) are:", "[\nx = \frac{-25 + \sqrt{817}}{2} \quad \ ext{and} \quad x = \frac{-25 - \sqrt{817}}{2}\n]", "Approximating numerically, since (\sqrt{817} \approx 28.6):", "- (x \approx \frac{-25 + 28.6}{2} = \frac{3.6}{2} = 1.8)\n- (x \approx \frac{-25 - 28.6}{2} = \frac{-53.6}{2} = -26.8)", "---", "### Why This Equation Matters", "Understanding how to simplify and solve quadratic equations like this one strengthens your ability to tackle real-world problems involving motion, optimization, and geometry. Mastering the quadratic formula and simplification techniques builds a strong foundation in algebra.", "---", "### Summary", "- Original equation: (600 + 60x + 40x + 4x^2 = 792)\n- Simplified: (4x^2 + 100x + 600 = 792)\n- Eventually becomes: (x^2 + 25x - 48 = 0)\n- Solutions using quadratic formula:\n [\n x = \frac{-25 \pm \sqrt{817}}{2}\n ]", "For further practice, try graphing the original quadratic function or exploring real-world applications like projectile motion or profit maximization — where quadratics often model key relationships.", "---", "Keywords: quadratic equation 600 + 60x + 40x + 4x² = 792, solve quadratic equation, simplify 4x² + 100x - 192 = 0, quadratic formula, x² + 25x - 48 = 0, real solutions quadratic, algebra practice.", "---", "Ready to solve more quadratics? Start by simplifying the equation and applying the quadratic formula today!"]