Question

Can someone walk me through how to make a trinomial a perfect square?

Answer 1

via completing the square method...give me a trinomial

Answer 2

The first one is x²+10x+c and we have to find the value of c

Answer 3

divide 10 by 2 what do you have?

Answer 4

add square of half the coefficient of x&y
referance sweart calculus sixth edition.

Answer 5

When you divide 10 by 2 you get 5.

Answer 6

now square that

Answer 7

what is \(5^2\)?

Answer 8

25

Answer 9

therefore, for x^2 + 10x + c to become a perfect square trinomial...c must be 25

Answer 10

because x^2 + 10x + 25 = (x+5)^2

got it?

Answer 11

I'm sorry.. I'm a really slow learner holy wow. Can we do a few until I get the hang of it? :)

Answer 12

sure

Answer 13

Thanks! :) Number 2 is x²-8x+c

Answer 14

okay..divide -8 by 2

Answer 15

So, it would be -4².. And c would equal 16. So the equation would be x²-8x+16?

Answer 16

YEP!!

Answer 17

Yay! Okay, so do you divide by 2 every single time?

Answer 18

not everytime...

Answer 19

just when you're finding the c

Answer 20

for example you are given x^2 + bx + 25 and find b

Answer 21

do you know how you can get it?

Answer 22

No..

Answer 23

okay...review!!

x^2 + 10x + c

how will you find c??

Answer 24

You divide by 2.

Answer 25

then..?

Answer 26

Square the quotient.

Answer 27

so you divide the middle term by 2..then square it...the result is the third term

so if you're given x^2 + bx + 25

this is reverse...

get the square root of 25..that gives you 5 then multiply it by 2!! yay

let me give you a formula

the general form is \(ax^2 + bx + c\)

when c is missing

\[(\frac{b}{2})^2 = c\] when b is missing \[\sqrt{2c}\] got it?

Answer 28

uhmm woops sorry \[b = 2\sqrt c\]

Answer 29

I don't have to deal with b though.. all the ones on my worksheet are with x's after the first 3.

Answer 30

Like, the next one says: Write each trinomial as a perfect square: x²+4x+4