Question

Find the solution(s) of x^2+3x-18=0

Answer 1

\[(x+6)(x-3) = 0\]

Answer 2

Two solutions were found :

x = 3
x = -6

Answer 3

Any questions?

Answer 4

How do you find the solutions?

Answer 5

cormacpayne and muzzack: good contributions. But would you kindly help the questioner find his or her own answers and do NOT find (let alone post) them for him/her yourself. We (or at least others on OpenStudy and I) want each experience a student has here on OpenStudy to be practice towards developing academic independence. Thank you.

Answer 6

You find the solutions by solving the equation.

Answer 7

How do I solve the equation?

Answer 8

Quinn33: You have various methods available to you to solve this quadratic equation. cormacpayne applied one of the more common ones: he / she factored the quadratic. Other methods include the quadratic formula, graphing, completing the square, and so on.

Could you copy down the original quadratic equation and factor it on your own, without help? If not, I'd suggest you ask questions and keep trying until you're able to do that.

Answer 9

You have to find the values of the variable that will make the equation a true statement.

Answer 10

I'm so lost.

Answer 11

Ok, let me explain. What is zero times any number equal?

Answer 12

0?

Answer 13

Yes you are right.

Answer 14

What value of x makes x-3 =0?

Answer 15

0?

Answer 16

Nope.

Solve for x in x-3=0.

What do you get?

Answer 17

3?

Answer 18

A Warm Welcome to Open Study. Stay Studious.

Answer 19

Correct. So that means if you replace x with 3 you will get the true statement 3 - 3 = 0 right?

Answer 20

right

Answer 21

So what are the solutions to (x - 3)(x + 6) = 0?

Answer 22

And the same idea holds for x + 6 = 0

Answer 23

3 and -6?

Answer 24

Yes, can you tell me why?

Answer 25

Not really.

Answer 26

What happens to (x - 3)(x + 6) = 0 when you replace x with 3?

Answer 27

Try it and find out :)

Answer 28

(x - 3)(x + 6) = 0

Let x =3

(3 - 3)(3 + 6) = 0

0(9) = 0 <----is this true?

Answer 29

yes it is true 0=0

Answer 30

Similarly, let x = -6 gives

(x - 3)(x + 6) = 0

(-6 - 3)(-6 + 6) = 0

-9(0) = 0 <---is this true?

Answer 31

Seeing that 0 = 0 in this case, to what conclusion can you come about x=-6 as a solution or not a solution of the given quadratic equation?

Answer 32

We know x = 3 or x = -6 are solutions of (x - 3)(x + 6) = 0

BECAUSE zero times any number is zero.

They are the only values of x that will make (x - 3)(x + 6) = 0 into a TRUE statement.

Answer 33

I'd like to recognize skullpatrol for doing such a good job of guiding Quinn towards finding his/her own answers, and for his excellent interpretation of those results at the end. Way to go, skullpatrol!

Answer 34

Thanks @mathmale :)