Question

In the function f(x) = 5(x2 − 4x + ____) + 15, what number belongs in the blank to complete the square?

Numerical Answers Expected!

Answer 1

4

Answer 2

why?

Answer 3

how did you get that?

Answer 4

you have -4x which is made up of -2x and -2x
now -2 times -2 = 4
thats why...

Answer 5

Solve 2x2 + 12x − 14 = 0 by completing the square.

2(x + 6)2 = 26; x = −6 + square root 13, x = −6 − square root 13

2(x + 6)2 = 20; x = −6 + square root 20, x = −6 − square root 20

2(x + 3)2 = 32; x = 1, x = −7

2(x + 3)2 = 32; x = 13, x = 19

Answer 6

x2 - 4x +4 = (x-2)(x-2) = (x-2)^2 this is completing the square

Answer 7

can you help me with that question too? please

Answer 8

so which answers would it be?

Answer 9

can u give it a try first :)

Answer 10

i want u to learn something here

Answer 11

umm well i don't think its a

Answer 12

first simplify it mate

Answer 13

2 ( x^2 + 6x - 7)

Answer 14

now u have +6x which is made up of +3x and +3x, so u have 3 and 3 , when u multiply them u get 9

Answer 15

ok

Answer 16

how do you make the -7 to a +9 ???

Answer 17

16

Answer 18

well done

Answer 19

so we get this, pay attention and tell me why did I put 32 outside, ok?

Answer 20

2( x^2 + 6x -7 + 16) - 32 = 0

Answer 21

2 (x^2 + 6x + 9) = 32

Answer 22

following me ???

Answer 23

yes

Answer 24

divide both side by 2 and factorize

Answer 25

(x+3)^2 = 16
what is x ?

Answer 26

5

Answer 27

one value for x is 1
the other is -7
why -7 though?
remember that when u Square a negative number u get a positive one, right ?

so the answer is...

2(x + 3)2 = 32; x = 1, x = −7


now why did u get 5 ??

Answer 28

i didn't pay attention the "2" was an exponent

Answer 29

Two sets of quadratic expressions are shown below in various forms.

Line 1: x2 + 3x + 2 (x + 1)(x + 2) (x + 1.5)2 − 0.25
Line 2: x2 + 5x + 6 (x + 2)(x + 3) (x + 2.5)2 + 6.25

Which line contains three equivalent expressions?

Line 1 only

Line 2 only

Both Line 1 and Line 2

Neither Line 1 nor Line 2

Answer 30

ok, so are you happy with this and do u understand it, or want to ask something about it? dont be shy to ask, ok?

Answer 31

no but i do have another question

Answer 32

in
Line 1: x2 + 3x + 2 = (x + 1)(x + 2)
and in
Line 2: x2 + 5x + 6 = (x + 2)(x + 3)

so you need to confirm the end bits of the lines if they are equivalent to the first 2, can u do that by yourself?

Answer 33

Two sets of quadratic expressions are shown below in various forms.

Line 1: x2 + 3x + 2 (x + 1)(x + 2) (x + 1.5)2 − 0.25
Line 2: x2 + 5x + 6 (x + 2)(x + 3) (x + 2.5)2 + 6.25

Which line contains three equivalent expressions?

Line 1 only

Line 2 only

Both Line 1 and Line 2

Neither Line 1 nor Line 2

Answer 34

is it line 1?

Answer 35

it could be both, you'll know once u expand the end bits

Answer 36

I'll help u with the first end bit, but u do the second one ok?

Answer 37

how do i do that then

Answer 38

(x + 1.5)2 − 0.25
(x+1.5)(x+1.5) - 0.25
x^2 + 1.5x + 1.5x + 2.25 - 0.25
x^2 + 3x + 2

now is this equivalent to x2 + 3x + 2 and (x + 1)(x + 2) ??

Answer 39

can u do the second one and show me?

Answer 40

no not really lol

Answer 41

lol..why

Answer 42

i dont knwo how

Answer 43

(x + 2.5)2 + 6.25
(x + 2.5)(x + 2.5) + 6.25
x^2 + 2.5x + 2.5x + 6.25 + 6.25

x^2 +5x + 12.5

and this is NOT equivaent to the previous
x2 + 5x + 6 and (x + 2)(x + 3)

Answer 44

so ur earlier guess of " Line 1 only" was correct but it was only a guess, u need to practice more on factorizing and simplifying if u want to be able to do maths with ease :)

Answer 45

okay thank you i have one last question

Answer 46

The cost to produce a product is modeled by the function f(x) = 5x2 − 70x + 258 where x is the number of products produced. Complete the square to determine the minimum cost of producing this product.

5(x − 7)2 + 13; The minimum cost to produce the product is $13.

5(x − 7)2 + 13; The minimum cost to produce the product is $7.

5(x − 7)2 + 258; The minimum cost to produce the product is $7.

5(x − 7)2 + 258; The minimum cost to produce the product is $258.

Answer 47

The cost to produce a product is modeled by the function f(x) = 5x2 − 70x + 258 where x is the number of products produced. Complete the square to determine the minimum cost of producing this product.

5(x − 7)2 + 13; The minimum cost to produce the product is $13.

5(x − 7)2 + 13; The minimum cost to produce the product is $7.

5(x − 7)2 + 258; The minimum cost to produce the product is $7.

5(x − 7)2 + 258; The minimum cost to produce the product is $258.

Answer 48

5(x − 7)2 + 13; The minimum cost to produce the product is $13.

5(x − 7)2 + 13; The minimum cost to produce the product is $7.

one of the above

Answer 49

is it the second one?

Answer 50

I think its the first one

Answer 51

i could be wrong tho, hold on

Answer 52

okay

Answer 53

damn...am confused, please ask someone else, do u mind?...sorry...