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: Move the constant term to the right side of the equation. The given equation is x^2 - 5x + 6 = 0. Subtract 6 from both sides: x^2 - 5x = -6 Step 2: Complete the square on the left side. To complete the square for an expression of the form x^2 + bx, we add ((b)/(2))^2. In this equation, b = -5. So, we need to add ((-5)/(2))^2 = ((25)/(4)) to both sides. Step 3: Add the value to both sides of the equation. x^2 - 5x + (25)/(4) = -6 + (25)/(4) Step 4: Factor the left side as a perfect square trinomial and simplify the right side. The left side factors as (x - (5)/(2))^2. For the right side, find a common denominator: -6 = -(24)/(4). (x - (5)/(2))^2 = -(24)/(4) + (25)/(4) (x - (5)/(2))^2 = (1)/(4) Step 5: Take the square root of both sides. sqrt((x - (5)/(2))^2) = ±sqrt((1)/(4)) x - (5)/(2) = ±(1)/(2) Step 6: Solve for x. Add (5)/(2) to both sides: x = (5)/(2) ± (1)/(2) This gives two possible solutions: x_1 = (5)/(2) + (1)/(2) x_1 = (6)/(2) x_1 = 3 And x_2 = (5)/(2) - (1)/(2) x_2 = (4)/(2) x_2 = 2 The solutions are x=2, x=3.