Question

What are the solutions of 2x2 + 8x = -26?

Answer 1

A) -2 ± 3i

B)-2 ± i

C)2 ± 6i

D)-3 ± 2i

Answer 2

\[2x^2+8x=-26~~~~~~~->~~~~~~~~~x^2+4x=-13\]

I divided everything by 2.

Answer 3

Now, how would you like to do it, by completing the square, quadratic formula?
(you can't really factor this)

Answer 4

how would i complete the square

Answer 5

You don't have to if you don't never done that before, but if you did and want/have to complete the square, add 4 to both sides.

Answer 6

if i were to do that would it be x^2 = -4x -13

Answer 7

Completing the square.

\[x^2+4x~=~-13\]\[~~~~~~~~+4~~~~~~~+4\]

\[x^2+4x+4=-9~~~~~~~~->~~~~~~~(x+2)^2~=~ (3i)^2\]

Can you do it now?

Answer 8

so lost hah...

Answer 9

Do you see how I added 4 to both sides?

Answer 10

yes

Answer 11

Alright, then do you see that \[x^2+4x+4\] factors into \[(x+2)(x+2)\]

which is same as \[(x+2)^2\]

Answer 12

yes

Answer 13

OK, so now I am showing a pre-step that would help you to square both sides.

I am FINDING the SQUARE ROOT of -9

Answer 14

\[-9~~= ~~(-1) \times 9 ~~=~~(i^2)~ \times ~3^2~=~(3i)^2\]

DO you follow how I found the square root of -9 ?

Answer 15

um i think so

Answer 16

Alrighty, but the thing is that the square root can be NEGATIVE OR POSITIVE, okay?

So it would be +-3i RIGHT ?

Answer 17

uhuh.

Answer 18

Lost?

Answer 19

no i think I'm starting to get it

Answer 20

Ok, so see how \[x^2+4x+4=-9~~~~~\] turns into \[(x+2)^2=~~(+-~3i)^2\]
which then after squaring both sides, turns into\[x+2=3i~~~~~or~~~~x+2=-3i\]

Answer 21

yeah

Answer 22

SO can you preform just the one final step for me? Please tell me your answer and what you did to get it?

Answer 23

alrigh

Answer 24

ok i would just subtract 2 from both swides so x=-2 +/- -3 ?

Answer 25

Yeap! COrrect, x= -2 +- 3i

Answer 26

thanks for the help

Answer 27

No problem!