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
To express x^2 + 6x + 17 in the form (x+p)^2 + q, we will use the method of completing the square. Step 1: Identify the coefficient of x. The expression is x^2 + 6x + 17. The coefficient of x is 6. Step 2: Complete the square for the x^2 and x terms. Take half of the coefficient of x and square it: ((6)/(2))^2 = 3^2 = 9. Add and subtract this value to the expression: x^2 + 6x + 9 - 9 + 17 Step 3: Group the perfect square trinomial and simplify the constants. The first three terms form a perfect square: (x+3)^2. (x^2 + 6x + 9) - 9 + 17 (x+3)^2 + 8 Step 4: Compare with the form (x+p)^2 + q. By comparing (x+3)^2 + 8 with (x+p)^2 + q, we can identify the values of p and q. p = 3 q = 8 The expression is (x+3)^2 + 8. The integer values are p = 3 and q = 8. Got more? Send 'em.