Question

x^2 + 3x = 0
Is this a special case, can it still be solved? If so, how? :) thanks!

Answer 1

Actualy you need this solved or factored?

Answer 2

factored is fine.

Answer 3

This equation is a quadratic equation. There are a good number of different ways in which you can solve quadratic equations. Remember any of them?

Answer 4

You want to factor? Go ahead. Please share your results.

Answer 5

Im currently just factoring and using the magix X method because those come easier for me

Answer 6

x^2+3x=0 is a special case in that there's no constant term.
Factoring will work. Factor x^2+3x=0 now, please.

Answer 7

But I don't know how to factor if I don't have a constant T-T

Answer 8

Next, set each of the 2 resulting factors = to 0 separately. Solve for x (2 different values).

Answer 9

Whether or not you have a constant for the 3rd term affects your ability to factor only by making the job easier. Look again. What do the 2 terms on the left have in common?

Factor x^2+3x=0.

Answer 10

Ok is it like this, (x+3) = 0
x = 0 and x = -3 >-<?

Answer 11

the x is what they have in common

Answer 12

True. But it appears that you have simply dropped the "x." Can't do that. Go back and try again: Factor x^2+3x=0 by factoring x out of the two terms on the left side.

Answer 13

x(x+3)(x+0) D:?

Answer 14

If you mult. that back together you get x^3+3x^2. Is that the same as what you started from?

Answer 15

No I think its just x(x+3) ?

Answer 16

You were right before: the 2 terms on the left are x(x+3).

Yes.

Set that = to 0 and solve for x (2 values).

Answer 17

x = 0 and x + 3 = 0
x = 0 and x + 3 = 0 -3
x = 0 and x = -3 >-<?

Answer 18

Yes, x=0 and x+3=0.
x+3=0-3 is incorrect; try re-writing it correctly. You must subtract 3 from both sides.

Answer 19

x + 3 = 0
-3 -3
x = -3 >->?

Answer 20

Better. Now, you have 2 possible solutions. What are they?

x=?
x=?

Answer 21

x = 0
x = -3 ?

Answer 22

Yes. Now check each solution in the original equation.
Let x=0 in the orig. eqn. Is the equation then true? or not?

Answer 23

Yes 0^2 + 0 = 0 ? D:

Answer 24

Yes. and what about x=-3?

Answer 25

-3^2 + -9 = 0
9 + -9 = 0 Yup

Answer 26

Therefore, you have solved this problem correctly. Very good!
Again, this quadratic is a special case because it lacks a constant term. But that does not prevent you from solving it by factoring; you could also use the quadratic formula (letting c=0).

Answer 27

Yeah it just makes it even easier. Thanks for helping me <3