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: Divide the entire equation by the coefficient of x^2. The given equation is 2x^2 - 13x + 15 = 0. Divide by 2: x^2 - (13)/(2)x + (15)/(2) = 0 Step 2: Move the constant term to the right side of the equation. x^2 - (13)/(2)x = -(15)/(2) Step 3: Take half of the coefficient of the x term, square it, and add it to both sides of the equation. The coefficient of x is -(13)/(2). Half of this is (1)/(2) × (-(13)/(2)) = -(13)/(4). Square this value: (-(13)/(4))^2 = (169)/(16). Add (169)/(16) to both sides: x^2 - (13)/(2)x + (169)/(16) = -(15)/(2) + (169)/(16) Step 4: Factor the left side as a perfect square trinomial and simplify the right side. The left side factors as (x - (13)/(4))^2. For the right side, find a common denominator: -(15)/(2) + (169)/(16) = -(15 × 8)/(2 × 8) + (169)/(16) = -(120)/(16) + (169)/(16) = (169 - 120)/(16) = (49)/(16) So the equation becomes: (x - (13)/(4))^2 = (49)/(16) Step 5: Take the square root of both sides. x - (13)/(4) = ±sqrt((49)/(16)) x - (13)/(4) = ±(7)/(4) Step 6: Solve for x. x = (13)/(4) ± (7)/(4) This gives two possible solutions: x_1 = (13)/(4) + (7)/(4) = (20)/(4) = 5 x_2 = (13)/(4) - (7)/(4) = (6)/(4) = (3)/(2) The solutions are x=5 or x=(3)/(2). Send me the next one 📸