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
Thanks for the clearer image, 10K! I can read this one now. Problem 18: To write 2x^2 + 12x - 2 in the form a(x+b)^2 - c, we use the method of completing the square. Step 1: Factor out the coefficient of x^2 from the terms involving x. 2x^2 + 12x - 2 = 2(x^2 + 6x) - 2 Step 2: Complete the square for the expression inside the parenthesis. Take half of the coefficient of x (which is 6/2 = 3) and square it (3^2 = 9). Add and subtract this value inside the parenthesis. 2(x^2 + 6x + 9 - 9) - 2 Step 3: Rewrite the perfect square trinomial. 2((x+3)^2 - 9) - 2 Step 4: Distribute the 2 to both terms inside the parenthesis. 2(x+3)^2 - 2 × 9 - 2 2(x+3)^2 - 18 - 2 Step 5: Combine the constant terms. 2(x+3)^2 - 20 Step 6: Compare this with the given form a(x+b)^2 - c. By comparing 2(x+3)^2 - 20 with a(x+b)^2 - c, we can identify the values of a, b, and c. a = 2 b = 3 c = 20 The values are a=2, b=3, c=20. 3 done, 2 left today. You're making progress.