Question

how do i solve 3x^2+x-2=0 by completing the sqaure?

Answer 1

idk, haha. My teacher doesnt explain how do these things very well. the homework says, Solve each equation by completing the square. \[3x ^{2}+x-2=0\]

Answer 2

& thats just one of them

Answer 3

alright well first you'd want to add 2 to the other side and divide by 3

Answer 4

then that'd leave \[x ^{2}+x=0\]

Answer 5

dont you add 2 to both sides of the equation?

Answer 6

add 2 to both sides... i mean't you want to put the 2 on the right side

Answer 7

so you should get
\[x^2+\frac{1}{3}x=\frac{2}{3}\]

Answer 8

then take your middle coefficient divide it by two and square it you should get 1/36 but remember you must add to both sides of the equation to keep the equality true

\[x+\frac{1}{3}x+\frac{1}{36}=\frac{2}{3}+\frac{1}{36}\]

Answer 9

ohhhhh then ?

Answer 10

now you have a perfect square on the left side so you can factor it

\[(x+\frac{1}{6})^2=\frac{2}{3}+\frac{1}{36}=\frac{25}{36}\]

Answer 11

now to solve for x, what would you want to do next?

Answer 12

still there?

Answer 13

hmmmmm..

Answer 14

hint* you can't solve for x when squared

Answer 15

idk D:

Answer 16

haha =] alright well we have so far this,

\[(x+\frac{1}{6})^2=\frac{25}{36}\]

in order to solve for x we need to get rid of the squared because we do not like it squared, because how would we be able to find the roots as is.

so what we need to do next is take the square root of both sides. doing this what do you get?

Answer 17

\[25\div36 \] how do we unsquare that?

Answer 18

\[\sqrt{(x+\frac{1}{6})^2}=\sqrt{\frac{25}{36}}\]

is this what you got so are you asking how we'd get rid of the square root?

Answer 19

yes

Answer 20

well using the square root rule that you should have learned and gone over

\[\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}\]

for all values >0

Answer 21

now you should be able to take the square root easily of the top and bottom

Answer 22

oh yes

Answer 23

ok well ithink igot it. thankyou !

Answer 24

np don't forget the positive and negative... you should get the answers to the factors (3x-2)(x+1) where x=-1,2/3