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
Welcome back — missed you this week. Step 1: Expand the right side of the equation. Given x^2 - 4x + 9 = (x+A)^2 + B. Expand (x+A)^2: (x+A)^2 = x^2 + 2Ax + A^2 So, the right side becomes: x^2 + 2Ax + A^2 + B Step 2: Compare coefficients. Equate the coefficients of the expanded right side with the left side x^2 - 4x + 9: For the x^2 term: 1 = 1 (matches) For the x term: 2A = -4 For the constant term: A^2 + B = 9 Step 3: Solve for A and B. From 2A = -4: A = (-4)/(2) = -2 Substitute A=-2 into A^2 + B = 9: (-2)^2 + B = 9 4 + B = 9 B = 9 - 4 B = 5 Thus, A=-2 and B=5. The correct option is D. The final answer is D. Send me the next one 📸