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: Identify the given equation. The equation is x^2 - 18x + 81 = 0. Step 2: Recognize the equation as a perfect square trinomial. A perfect square trinomial has the form a^2 - 2ab + b^2 = (a-b)^2. In this equation, a^2 = x^2 (so a=x), and b^2 = 81 (so b=9). The middle term is -18x, which matches -2ab = -2(x)(9) = -18x. Step 3: Factor the trinomial. Using the perfect square trinomial formula, we can rewrite the equation as (x-9)^2 = 0. Step 4: Solve for x. Take the square root of both sides: sqrt((x-9)^2) = sqrt(0). This simplifies to x-9 = 0. Add 9 to both sides: x = 9. x^2 - 18x + 81 = 0 (x-9)^2 = 0 x-9 = 0 x = 9 The value of x is 9. Got more? Send 'em 📸