What must be added to the following binomials to make them perfect square trinomials?

Question

hello anyone can you help me about this problem..because i don't know how to answer it this question...

here's my question

x^2-10x+___ what must be added to this question to get the blank answer?...

x^2+6n+___

x^2-12x+____

x^2+7y+____

x^2+30m+_______

x^2-3b+___

x^2-11d+___

x^2-5s+____

x^2-4/5x+____

x^2+1/3x+_____?

please help me about this thanks

Answer 1

quadratics are in form ax^2 + bx + c = 0. here we aren't using the 0, and you are trying to form a perfect square so it factors to (x+n)^2.

to do this you take the b value, or in the first questions case, the -10. Divide it by two to get -5. Then square this to get your c value. Now you can factor it into a perfect square.

Answer 2

Since all of the first terms are x^2, ignore them for now...

Go to the next term.  It doesn't matter whether it is positive or negative.

Pull out the number in front of the variable in the 2nd term

Multiply it by 1/2

Square the result

The answer to that is the number that makes it a perfect square trinomial.

for example : x^2 - 10x

10/2 = 5.......5^2 = 25......so 25 goes in the blank

x^2 - 3b

3/2 = 1.5.....1.5^2 = 2.25....so 2.25 goes in the blank

x^2 + 1/3x

1/3 * 1/2 = 1/6........(1/6)^2 = 1/36.....so 1/26  goes in the blank

Good luck to you !