How do you complete the square of y = x²- 5x- 14

I'll start you off but, I won't do your homework for you totally.
(x-7)(x+2)


Here's the explanation of how I got the above. You need to find two numbers that multiply together to get 14 and when you subtract or add them, equal 5. The only factors for 14 are 1 & 14 and 2 & 7.
Since the symbol before 14 is a - sign, you know that means that one will have a plus sign an and the other a minus sign.
So, since 7 minus 2 is five, we know that those are the two numbers to choose.
We know to make the 7 the one with the minus sign in front of it because in the original equation the minus sign is in front of the 5x.

using the above explanation

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x ^2 - 5x - 14
(x - 5/2)^2 - 25/4 - 14 = 0
(x - 5/2)^2 = 81/4
x - 5/2 = +/- Sqrt 81/4
x - 5/2 = +/- 9/2
x = 5/2 + 9/2 = 14/2 = 7
x = 5/2 - 9/2 = - 4/2 =- 2

y=x^2-5x-14
=x^2-5x+25/4 -14 -25/4
=(x-5/2)^2 - 81/4

y=(x+2)(x-7)

factor
(x-7)(x+2)
X-7=0 x+2=0
x=7 x=-2
x=7, or -2

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