Question

help in creating a perfect square trinomial

Answer 1

x^2-5x+k

Answer 2

I've been trying every number, but I can't seem to figure out a number that will make it a perfect square tronimal

Answer 3

what is half of -5?

Answer 4

it's -2.5

Answer 5

yes, now square (-2.5)^2

Answer 6

btw, you can also write that as -5/2

Answer 7

I'm sorry but I don't understand how I will square it. Like why is that necessary?

Answer 8

when you square (-2.5)^2 = (-2.5)(-2.5) = 6.25

or same as

(-5/2)(-5/2) = 25/4

then
x^2 -5x + (25/4) >> hence, k= 25/4
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Let's check

\[(x-\frac{5 }{ 2})^2\]

remember to factor this, you use x^2 +2ab +b^2

\[= x^2 +(2)(1) \frac{ -5 }{ 2 }x + \frac{ 25 }{ 4 }\]

\[= x^2 -5x + \frac{ 25 }{ 4 }\]

Answer 9

aaaah ok. so then that concludes that K will be 25/4

Answer 10

to answer your question,

remember when you factor

(a+b)^2 = a^2 + 2ab +b^2

similar to x^2 -5x +k
--------------
when you compare those two equations
x^2 = a^2
a=1, since x does not have a number infront, (for ex. if 3x^2 ,then a=3 // if 4x^2, then a=4, etc.)

2ab= -5x >>plug in a=1
2(1)b= -5x
b= -5/2

now, k= b^2

k= (-5/2)^2
k= 25/4= 6.25

This is just working backwards with the equation.

Answer 11

hope this helps :)

Answer 12

@study100 ah ok, thank you, i appreciate your time to help me out:)

Answer 13

you're welcome! Concepts > right answer.