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Math Help - Can this equation be factored?

  1. #1
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    Can this equation be factored?

    X^2 + 210x -9,000 = 0
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    MHF Contributor Siron's Avatar
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    Re: Can this equation be factored?

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

    Can you do that?
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    Re: Can this equation be factored?

    Quote Originally Posted by benny92000 View Post
    X^2 + 210x -9,000 = 0
    Have a look at this.
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    Re: Can this equation be factored?

    Use the discriminant: b^2-4ac

    If it is a square number then the equation will factor
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    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.
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    MHF Contributor Siron's Avatar
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    Re: Can this equation be factored?

    Why do you need a square number for your Discriminant? If  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: D=80100=30\sqrt{89}
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    Re: Can this equation be factored?

    Read 3 posts above^. I was responding to that.
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    Re: Can this equation be factored?

    Quote Originally Posted by Siron View Post
    Why do you need a square number for your Discriminant? If  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: D=80100=30\sqrt{89}
    If \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.

    Quote 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.
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    MHF Contributor Siron's Avatar
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    Re: Can this equation be factored?

    Ok, do you have the right answer now? ...
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    Re: Can this equation be factored?

    hi benny,are you sure that your equation should have a minus sign in front of 9000?
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    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.
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    Re: Can this equation be factored?

    Quote Originally Posted by benny92000 View Post
    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.
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    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?
    Last edited by benny92000; August 3rd 2011 at 01:13 PM.
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    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.
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    Re: Can this equation be factored?

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

    and use the difference of two squares formula to factorise.
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