This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Hey Young, good to see you again. Step 1: Identify the form of a perfect square. A quadratic expression in the form x^2 + Bx + C is a perfect square if it can be written as (x+k)^2. Expanding (x+k)^2 gives x^2 + 2kx + k^2. Step 2: Compare the given expression with the perfect square form. The given expression is x^2 + 10x + c + 2. Comparing coefficients with x^2 + 2kx + k^2: The coefficient of x is 10, so 2k = 10. The constant term is c+2, so k^2 = c+2. Step 3: Solve for k. From 2k = 10, we find k: k = (10)/(2) k = 5 Step 4: Solve for c. Substitute the value of k into the equation for the constant term: k^2 = c+2 5^2 = c+2 25 = c+2 Subtract 2 from both sides to find c: c = 25 - 2 c = 23 The value of c is 23. Send me the next one 📸