Question

Solve 3x^{2}+4x-4=0 by completing the square. Please explain the steps please. I got lost in the part where you're supposed to divide by 2 and square b?

Answer 1

can someone help @amistre64 @Hero @ash2326 @experimentX

Answer 2

first make the co-efficient of x^2 as 1
by dividing both sides by 3, what u get ?

Answer 3

correct, so now your co-efficient of x = b = 4/3, divide it by 2, what u get ?

Answer 4

2/3

Answer 5

I don't understand what I have to do for the rest of the problem @hartnn

Answer 6

now square that, what u get ?

Answer 7

you're not supposed to square root? uh, 4/9

Answer 8

no, not square root, u need to square it,
and 4/9 is correct!
so , now add 4/9 on both sides, what u get ?

Answer 9

x^2 + 4/3x+4/9 = -8/9

Answer 10

correct .
now u notice that left side is a perfect square and can be written in the form (x+a)^2
can u write it in that form ?

Answer 11

I need to go, I'll check back later :(

Answer 12

no problem.

Answer 13

is this problem an unfinished business?

Answer 14

I don't understand, so (x+x^2)?
@sirm3d yeah, I'm still confused on how to solve the rest of the problem :(

Answer 15

the left side of the equation should now be \[\left( x+\frac{ 2 }{ 3 } \right)^{2}\]

Answer 16

the trick is to get the square root of the first and last terms of the left side of the equation
enclose by a paor of parenthesis, and square it

Answer 17

so I set that left side you gave me and the right to = -8/9

Answer 18

It's confusing because I had to turn the 2/3^2 to a 4/9 before and now I'm changing it back? @sirm3d

Answer 19

it is necessary in completing squares

Answer 20

you have to square (2/3) to get a perfect square trinomial expression on the left side of your equation

Answer 21

\[(x+2/3)^2=-8/9\]

Answer 22

it would be an i number for the square root of -8/9?

Answer 23

yes

Answer 24

\[x+2/3=i 0.942809042

Answer 25

\[x+2/3=i0.942809042\]

Answer 26

that doesn't look right..

Answer 27

\[x+\frac{ 2 }{ 3 }=\pm \frac{ 2i \sqrt{2} }{ 3 }\]

Answer 28

x_x any little short explanation on how you got the right side?

Answer 29

you're literally saving my life right now lol (I have a quiz tomorrow morning, well today actually cause it's 4am and I'm still awake from a trippy halloween)

Answer 30

the square root of a fraction is a fraction of square roots
\[\sqrt{\frac{ 8 }{ 9 }}=\frac{ \sqrt{8} }{ \sqrt{9} }\]

Answer 31

the i number is necessary because the right side is negative, -8/9

Answer 32

Oh! so you do each separate not as a whole.

Answer 33

I could just leave that as my final answer since both are gonna be imaginary right?

Answer 34

yes

Answer 35

Thank you so much!

Answer 36

it would be best to direct that question to your teacher, since he/she will be the one to check answers