what is the third term necessary to make this a perfect square trinomial?
what is the binomial quantity squared it is equivalent to?
x^2 - 9x _______= (________)^2
x^2 + 10x _______= (________)^2
since (a-b)^2 = a^2-2ab+b^2, just divide the middle coefficient by 2 and square it.
(9/2)^2
and
5^2
To determine the missing third term and the binomial quantity squared, we can use the concept of completing the square.
For the first equation, x^2 - 9x + __, to make it a perfect square trinomial, we need to find the value that completes the square. To do this, we take half of the coefficient of the middle term (-9x) and square it.
In this case, half of -9x is -4.5x, and when squared, we get 20.25. Therefore, the missing third term is 20.25.
So, x^2 - 9x + 20.25 = (x - 4.5)^2.
For the second equation, x^2 + 10x + __, we follow the same process. Half of the coefficient of the middle term (10x) is 5x, and when squared, we get 25. Therefore, the missing third term is 25.
So, x^2 + 10x + 25 = (x + 5)^2.