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
Here are the solutions to the quadratic equations: 1) Solve 3x^2 - 27 = 0 Step 1: Factor out the common term, which is 3. 3(x^2 - 9) = 0 Step 2: Recognize the difference of squares, x^2 - 9 = x^2 - 3^2. 3(x - 3)(x + 3) = 0 Step 3: Set each factor containing x to zero and solve for x. x - 3 = 0 x = 3 x + 3 = 0 x = -3 The solutions are x = 3, -3. 2) Solve 2x^2 + x - 300 = 0 Step 1: Find two numbers that multiply to 2 × (-300) = -600 and add up to the middle coefficient, which is 1. The numbers are 25 and -24. 25 × (-24) = -600 25 + (-24) = 1 Step 2: Rewrite the middle term (x) using these two numbers. 2x^2 + 25x - 24x - 300 = 0 Step 3: Factor by grouping the terms. x(2x + 25) - 12(2x + 25) = 0 Step 4: Factor out the common binomial term (2x + 25). (2x + 25)(x - 12) = 0 Step 5: Set each factor to zero and solve for x. 2x + 25 = 0 2x = -25 x = -(25)/(2) x - 12 = 0 x = 12 The solutions are x = -(25)/(2), 12. Send me the next one 📸