At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
Hints: Completing the square: step 1: divide the whole expression by the coefficient of x^2, So if we have 2x^2+8x+...., we rewrite as 2(x^2+4x+...) In these cases, the coefficients are both one, so we're ready for step 2. step 2: Work inside the brackets: the constant term required to complete the square is half of the coefficient of x, all squared. Example: 3(x^2+6x+K) then K=(6/2)^2=9 and we have a perfect square: 3(x^2+6x+9) =3(x+3)^2 or x^2-7x+.... =x^2-7x+(7/2)^2 =(x^2-7/2)^2
@Bookworm14 are you there?
sorry @mathmate My computer froze im going to look over this now
Is it 1. A 2. D @mathmate
Did you work those answers out? If you did, you would realize that the constant term you add is equal to ( half the coefficient of x )^2. Whether the coefficient of x is positive or negative, the square is always positive. One more thing, when you check your answer, I would like you to type out the answer and CHECK your own answer as you type it out. This will reduce mistakes because you will check it one more time, and you will have to be responsible for the answer.
#1 x^2 - 11x + ___ -11 /2 = -5.5 -5.5^2 = -30.25 OR -121/4 x^2-11x+ (-121/4) Ohh its positive because I squared it? so it should be positive 121/4 ?? #2 x^2+19x+___ 19/2 = 9.5 9.5 ^2 = 90.25 OR 361 / 4 x^2 + 19x + 361/4 Is this how it is done or no?
@TheSmartOne @jim_thompson5910 is the correct answer for these 1. D 2. D or am i wrong again?
One more thing, when you check your answer, I would like you to type out the answer and CHECK your own answer as you type it out. This will reduce mistakes because you will check it one more time, and you will have to be responsible for the answer.
@bookwork14 Remember, when you square the product of two numbers, both are squared. for example, \((ab)^2=a^2b^2\) Similarly, (-2)^2=(-2)*(-2)=(-1)(-1)(2)(2)=+4. In completing the square, the constant is always added on because of the squaring.
So, D and D are correct.
Fwew, alright I think I am getting the hang of this now! Thank you!
Well done! You're welcome! :)