Question

solve the quadratic equation by completing square
z^2 +16z + 47 =0

a. z=-8+/-sqrt17 b. z=8+sqrt17 c. z= -16 +sqrt47 d. z=8 +/- sqrt47

Answer 1

so z has a coefficient of 1

Answer 2

so we dont have to worry about it

Answer 3

i guess you prolly already know that a=1, b=16, and c=47

Answer 4

but you get all the z's on one side, and the constants on the other, so you rearrange it so now the equation looks like this:
z^2 + 16z = -47

Answer 5

now take half of the b coefficient, so (16/2) and square it, so (16/2)^2
so 8^2 = 64

Answer 6

add that to both sides of your new equation

Answer 7

so now you got z^2 + 16z + 64 = -47 + 64

Answer 8

now you can simplify that so its z^2 + 16z +64 = 17

Answer 9

now FOIL that equation on the left side there...which is simply (z + 8) (z + 8)

Answer 10

cuz that will make z^2 + 16z + 64 again

Answer 11

so basically you have (z + 8) ^2 = 17

Answer 12

so to get rid of the ^2 just take the square root of both sides

Answer 13

now u got z + 8 = sq. root 17

Answer 14

so then it would be -8=.- sqrt 17 is that right?

Answer 15

right...i was just a bit confused by your choice of answers there, but obviously C and D are wrong and since you would subtract 8 to get z by itself then there has to be a -8 in the answer, so yeah A is the right answer...maybe i'm just confusing myself cuz its written on a computer and not on paper lol

Answer 16

lol thanks a bunch