Question

-49x^2 +35x +14 = 0

i tried the formula and ended up with a huge number under the square root. if i complete the square then i will end up with huge fractions. any body have knowledge on this. i will not be permitted to use a calculator on the test. we will only have a pencil and paper.

Answer 1

do you know the trick how to factorize?

Answer 2

ax^2+bx+c=0

Answer 3

i did not focus on factoring because the formula and completing the square yield 100% results for all quadratic problems . i do need to learn how to factor polynomials thought. can you help ?

Answer 4

yes

Answer 5

it's very easy

Answer 6

by which method you need to find it? Completing the square?

Answer 7

preferably . however, i will use any method that gets the answer quickest. i will only have approximately 1.25 minutes on each problem during the test ...

Answer 8

completing the square: multiply each side by -1, to get the x^2 positive

Answer 9

i thought you had to have a coefficient of 1 for A to use this method ..

Answer 10

so it will be \[49x ^{2}-35x-14\]=0

Answer 11

(7x-5/2)^2-81/4

Answer 12

=0

Answer 13

move 81/4 to the o side, so it will be \[(7x-\frac{ 5 }{ 2 })^{2}=\frac{ 81 }{ 4 }\]

Answer 14

remove square, so it will be 7x-5/2=9/2

Answer 15

could you show the way you managed : (7x-5/2)^2-81/4=0 ?

Answer 16

seems to be you are not enough familiar with completing the square

Answer 17

i did not focus on factoring when i was learning how to solve quadratics
so, i hardly know how to do it.

Answer 18

do you know the formula of completing the square

Answer 19

it's not factoring, it is completing the square

Answer 20

divide b by 2, square the answer and add it to the Ax^2 + Bx

the way it was shown to me, was to subtract b from the result and add the difference to both sides of the equation to keep the values down to a manageable size :)

so it would work like this is b was 4 and c was 6:

4/2 = 2
2^2 = 4
6-4 = 2

Ax^2 +4x + 6 = 2

Answer 21

then take a and c to form :

(x+6)^2 = 2

Answer 22

that is what i know about completing the square :)

Answer 23

oh yeah:

x+6=√(2)
x=√(2) - 6

Answer 24

whats that

Answer 25

the answer, so i had thought.

Answer 26

you mean of -49x^2 +35x +14 = 0????

Answer 27

do you want me to explain how completing the square works

Answer 28

yes, because what i have learned this far is not working :(

Answer 29

\[(a+b)^{2}=a ^{2}+2ab+b ^{2}\]

Answer 30

remember?

Answer 31

yes, i have that in my notes

Answer 32

so, in many quadratic equations it's not always in that way. so so add and substract additional values

Answer 33

for example take as (x+2)^2 as our equation

Answer 34

i took (x+2)^2 to make it simpler

Answer 35

so \[(x+2)^{2}=x ^{2}+2*2*x+4\]

Answer 36

and in questions you get problems like x^2+4x+13, and not 4

Answer 37

i worked out the math once and found that relationship to be true using a calculator, however, i failed to comprehend the relationship.

Answer 38

so you need to reformulate it in the other form to x^2+4x+4+9

Answer 39

did you get that?

Answer 40

4+9=13

Answer 41

so you can complete the square -----> \[(x+2)^{2}+9\]

Answer 42

what happened to the 4 ?
x^2+4x+13
x^2+4x+4+9
(what happened in between?)
(x+2)^2+9

Answer 43

we know that (x+2)^2=x^2+4x+4

Answer 44

so the rule of completing the square derived from this

Answer 45

(x+2)^2 converts to x^2 + 4 . i do not comprehend how the 4x works into this. o_O

Answer 46

imagine if you were given a question like this \[x^{2}+4x+13\] and asks to complete the square

Answer 47

you know that \[(x+2)^{2}=x^{2}+4x+4\]

Answer 48

so you can reformulate it in the form of \[x ^{2}+4x+13=x^{2}+4x+4+9\]

Answer 49

substitute our square into that

Answer 50

we will get the new equation of \[(x+2)^{2}+9\]

Answer 51

so how we can derive the formula using so simple method?

Answer 52

i guess i will simply have to learn more about factoring polynomials because i am not comprehending this. thanks for trying :)

Answer 53

in short, formula is like that \[ax ^{2}+bx+c\]

Answer 54

where \[b=2*\sqrt{a}*\sqrt{c}\]

Answer 55

\[(\sqrt{a}*x+\frac{ b }{ 2\sqrt{a} })^{2}\]