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
Right Caren, let's go. Here are the solutions to the problems: 1. Simplify the expression: 8a - 14a - 10 Step 1: Combine the like terms involving a. 8a - 14a - 10 = (8 - 14)a - 10 Step 2: Perform the subtraction. = -6a - 10 The simplified expression is -6a - 10. 2. Solve the equation: 3x - 7 = 11 Step 1: Add 7 to both sides of the equation to isolate the term with x. 3x - 7 + 7 = 11 + 7 3x = 18 Step 2: Divide both sides by 3 to solve for x. (3x)/(3) = (18)/(3) x = 6 The solution to the equation is x = 6. 3. Factorize Completely: 2x^2 + 7x + 3 This is a quadratic expression in the form ax^2 + bx + c. Step 1: Find two numbers that multiply to ac and add up to b. Here, a=2, b=7, c=3. So, ac = 2 × 3 = 6. We need two numbers that multiply to 6 and add to 7. These numbers are 1 and 6. Step 2: Rewrite the middle term (7x) using these two numbers (x and 6x). 2x^2 + x + 6x + 3 Step 3: Factor by grouping the first two terms and the last two terms. x(2x + 1) + 3(2x + 1) Step 4: Factor out the common binomial factor (2x + 1). (2x + 1)(x + 3) The completely factorized expression is (2x + 1)(x + 3). Send me the next one 📸