L'équation est \( (15 + 2x)(10 + 2x) = 264 \).

["How to Solve the Equation ( (15 + 2x)(10 + 2x) = 264 ): A Step-by-Step Guide", "Are you struggling to solve quadratic equations like ( (15 + 2x)(10 + 2x) = 264 )? This article breaks down the process clearly, helping you understand how to expand, simplify, and solve such equations efficiently using algebraic techniques.", "---", "### Understanding the Equation", "We start with the equation:", "[\n(15 + 2x)(10 + 2x) = 264\n]", "This equation represents the product of two binomials equal to 264. Our goal is to simplify it into a standard quadratic form and solve for ( x ).", "---", "### Step 1: Expand the Left Side", "Use the distributive property (also known as FOIL) to expand:", "[\n(15 + 2x)(10 + 2x) = 15 \cdot 10 + 15 \cdot 2x + 2x \cdot 10 + 2x \cdot 2x\n]", "Calculating each term:", "- ( 15 \cdot 10 = 150 )\n- ( 15 \cdot 2x = 30x )\n- ( 2x \cdot 10 = 20x )\n- ( 2x \cdot 2x = 4x^2 )", "Add all terms:", "[\n150 + 30x + 20x + 4x^2 = 4x^2 + 50x + 150\n]", "So the equation now is:", "[\n4x^2 + 50x + 150 = 264\n]", "---", "### Step 2: Move All Terms to One Side", "Subtract 264 from both sides to form a standard quadratic equation:", "[\n4x^2 + 50x + 150 - 264 = 0\n]\n[\n4x^2 + 50x - 114 = 0\n]", "---", "### Step 3: Simplify the Quadratic Equation", "To make calculations easier, divide every term by 2:", "[\n2x^2 + 25x - 57 = 0\n]", "This is now in standard form:", "[\n2x^2 + 25x - 57 = 0\n]", "---", "### Step 4: Solve Using the Quadratic Formula", "Since factoring may be difficult, use the quadratic formula:", "[\nx = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\n]", "For our equation ( 2x^2 + 25x - 57 = 0 ), the coefficients are:", "- ( a = 2 )\n- ( b = 25 )\n- ( c = -57 )", "Calculate the discriminant:", "[\nb^2 - 4ac = 25^2 - 4(2)(-57) = 625 + 456 = 1081\n]", "Since ( 1081 ) is a positive number but not a perfect square, the solutions are irrational:", "[\nx = \frac{-25 \pm \sqrt{1081}}{4}\n]", "---", "### Step 5: Final Answer", "The two solutions are:", "[\nx = \frac{-25 + \sqrt{1081}}{4} \quad \ ext{and} \quad x = \frac{-25 - \sqrt{1081}}{4}\n]", "---", "### Additional Tips: Checking Real-World Context", "Equation like ( (15 + 2x)(10 + 2x) = 264 ) may represent applied problems — such as modeling area growth or financial projections. Always verify your solution by plugging back into the original equation to ensure accuracy.", "---", "### Summary", "- Expand the binomials using the distributive property.\n- Simplify into standard quadratic form.\n- Solve using the quadratic formula when factoring is complex.\n- Interpret your answer critically.", "Solving equations like ( (15 + 2x)(10 + 2x) = 264 ) becomes easier with practice and proper algebraic tools — unlock the power of algebra today!", "---", "Keywords: solve ( (15 + 2x)(10 + 2x) = 264 ), quadratic equation solving steps, expand ( (15 + 2x)(10 + 2x) ), quadratic formula example, algebra tutorial, solving binomial equations.", "---", "Ready to master more algebra? Explore related topics like completing the square, quadratic inequalities, or real-world equation applications to strengthen your math skills!"]