Thread: Can this equation be factored?

1. Can this equation be factored?

X^2 + 210x -9,000 = 0

2. Re: Can this equation be factored?

Yes, use the quadratic formula, you'll find two different zero's $\displaystyle x_1$ and $\displaystyle x_2$ therefore the quadratic equation can be factorized as (in general):
$\displaystyle ax^2+bx+c=a(x-x_1)\cdot(x-x_2)$

Can you do that?

3. Re: Can this equation be factored?

Originally Posted by benny92000
X^2 + 210x -9,000 = 0
Have a look at this.

4. Re: Can this equation be factored?

Use the discriminant: $\displaystyle b^2-4ac$

If it is a square number then the equation will factor

5. Re: Can this equation be factored?

I am not getting a square number when I plug it in with my calculator. Siron, I tried factoring it earlier and I didn't come up with the right answer.

6. Re: Can this equation be factored?

Why do you need a square number for your Discriminant? If $\displaystyle D>0$ then you can take the square root of it, no matter if it's a square number or not, or I don't understand what you're meaning.

You'll get: $\displaystyle D=80100=30\sqrt{89}$

7. Re: Can this equation be factored?

Read 3 posts above^. I was responding to that.

8. Re: Can this equation be factored?

Originally Posted by Siron
Why do you need a square number for your Discriminant? If $\displaystyle D>0$ then you can take the square root of it, no matter if it's a square number or not, or I don't understand what you're meaning.

You'll get: $\displaystyle D=80100=30\sqrt{89}$
If $\displaystyle \Delta > 0$ then there are two real solutions but it doesn't state whether or not they're rational.

If it's a square number then it will factor over the rational numbers which is generally why equations are factored.

Originally Posted by OP
I am not getting a square number when I plug it in with my calculator.
That means it won't factor over the rational numbers. The discriminant is positive so there are still two real solutions.

9. Re: Can this equation be factored?

Ok, do you have the right answer now? ...

11. Re: Can this equation be factored?

I am actually working with a long word problem, so I will give you guys the word problem. I am positive there should have been a minus sign. I know the correct answer to this problem. I just can't make sense of it.

Info: A park is going to be made on unused land that a city owns. The park will be a rectangular region 60 feet by 150 feet with an area of 9,000 square feet.
Problem: The long term plan for the park involves doubling the area of the park. The length and width of the park will each be extended by d feet. For which of the following equations is x=d a solution?

A. (x + 60)(x + 150) = 2(9,000) This is the correct answer.

I have mused over this problem for over 20 minutes (obviously to no avail). I think I am fundamentally misunderstanding the question.

12. Re: Can this equation be factored?

Originally Posted by benny92000
I am actually working with a long word problem, so I will give you guys the word problem. I am positive there should have been a minus sign. I know the correct answer to this problem. I just can't make sense of it.

Info: A park is going to be made on unused land that a city owns. The park will be a rectangular region 60 feet by 150 feet with an area of 9,000 square feet.
Problem: The long term plan for the park involves doubling the area of the park. The length and width of the park will each be extended by d feet. For which of the following equations is x=d a solution?

A. (x + 60)(x + 150) = 2(9,000) This is the correct answer.

I have mused over this problem for over 20 minutes (obviously to no avail). I think I am fundamentally misunderstanding the question.

Your equation is fine and so is the method used to derive it. Solve the quadratic using the quadratic formula, you won't get a rational answer but you'll get an answer.

13. Re: Can this equation be factored?

I still don't understand how/why it is the correct answer.

I'm confused about the x=d solution. Isn't x the same as D for both the length and width?

Wouldn't x have to be a rational number to qualify as a solution?

14. Re: Can this equation be factored?

It appears that you had a number of equations to choose from. This one DOES describe the solution to the problem. (If you solve for x and then let d = x, where x is that solution, then adding that value of d to both the length & width will double the area of the park.

There is nothing in this problem that says d has to be rational. In fact, no rational value of d will work. (any rational value for d that's greater than 15 sqrt(89)-105 will more than double the area.)

BTW: It also appears that the intent of the exercise was to see if you could set-up an equation which could be used to solve the problem, rather than to actually follow through with the solution.

15. Re: Can this equation be factored?

Originally Posted by benny92000
X^2 + 210x -9,000 = 0
Complete the square: (x + 105)^2 - ...... = 0

and use the difference of two squares formula to factorise.