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 quadratic equation. The given equation is x^2 + 7x + 10 = 0. To factorize this, we need to find two numbers that multiply to the constant term (10) and add up to the coefficient of the middle term (7). Step 2: Find the two numbers. The two numbers that satisfy these conditions are 2 and 5, because 2 × 5 = 10 and 2 + 5 = 7. Step 3: Rewrite the middle term using these numbers. Rewrite 7x as 2x + 5x: x^2 + 2x + 5x + 10 = 0 Step 4: Group the terms and factor out common factors. Group the first two terms and the last two terms: (x^2 + 2x) + (5x + 10) = 0 Factor out x from the first group and 5 from the second group: x(x + 2) + 5(x + 2) = 0 Step 5: Factor out the common binomial. Notice that (x + 2) is a common factor: (x + 2)(x + 5) = 0 Step 6: Set each factor to zero to solve for x. For the product of two factors to be zero, at least one of the factors must be zero. x + 2 = 0 or x + 5 = 0 Solving for x in each case: x = -2 or x = -5 The solutions for the equation are: x = -2, x = -5 Send me the next one 📸