Given that F(x) = X^2 - 10X + 17. Write F(x) in the form of (x+a)^2 + b = 0, where a, & b are constants.

So we know that our equation is: X² - 10X +17 = 0. STEP 1: rearrange this equation to get x on one side: X² - 10X = -17. Lets call this, "equation 1". STEP 2: Understand that (X + a)² = X² + 2aX + a². Comparing the terms with equation 1, we can see that 2aX = -10 meaning that a = -5. STEP 3: Understand that (X - 5)² = X² - 10X +25. STEP 4: Rearranging the equation to match the left hand side of equation 1 gives: X² - 10X = (X - 5)² - 25. STEP 5: substituting that into equation 1 gives: (X - 5)² - 25 = -17 Therefore, (X - 5)² - 8 = 0 . Hence, a = -5 & b= -8