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
Step 1: The problem asks to solve for 'x' in the equation: x² - 14x + 49 = 0 Step 2: This is a quadratic equation in the form ax² + bx + c = 0, where a=1, b=-14, and c=49. We can solve this by factoring, completing the square, or using the quadratic formula. This equation looks like a perfect square trinomial. Step 3: A perfect square trinomial has the form (px + q)² = p²x² + 2pqx + q². In our equation, x² - 14x + 49 = 0: p² = 1, so p = 1. q² = 49, so q = ±7. 2pq = 2(1)(q) = 2q. We need 2q to be -14, so q = -7. This matches q² = (-7)² = 49. Step 4: So, the equation can be rewritten as: (x - 7)² = 0 Step 5: To solve for x, take the square root of both sides: √(x - 7)² = √0 x - 7 = 0 Step 6: Add 7 to both sides: x = 7 The solution is x = 7. Got more? Send 'em 📸