Question

(x + 2)(3x) = (x + 2)(6)

Answer 1

distribute on both sides

Answer 2

3x^2 + 6x = 6x + 12

Answer 3

good, now subtract 6x from each side

Answer 4

3x^2 = 12

Answer 5

good, now divide both sides by 3

Answer 6

x = 2

Answer 7

right?

Answer 8

almost, don't forget x = -2 as well

x = 2 and x = -2

Answer 9

wait, how?

Answer 10

when we solve

x^2 = A, we must take into account the positive and negative square roots

Answer 11

but if its squared doesnt it turn positive?

Answer 12

right, that's precisely why we need to take both positive and negative roots

Answer 13

can you type it out so i can see?

Answer 14

allow me to explain

Answer 15

we got down to

x^2 = 4, right?

Answer 16

right

Answer 17

you found x = 2, which works when we substitute back into the equation

x^2 = 4

2^2 = 4

Answer 18

notice what happens when we let x = -2 instead

x^2 = 4

(-2)^2 = 4

4 = 4

therefore, x = -2 is also a solution.

Answer 19

ohhhhh..... but is that how I figure it out in every situation, or is there a way so it becomes part of the routine of solving the problem?

Answer 20

in general:



this is a tricky concept