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Old November 6th, 2009, 03:08 PM
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Default Quadratic eq., solve for x when first variable is not 1

2x^2 - 3x - 5 = 0

I'm lost as to how I get rid of the 2 in 2x^2 so that it's x^2. I keep getting fractions that have very high LCDs.
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Old November 6th, 2009, 03:17 PM
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2x^2-3x-5 =(x+1)(2x-5)
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Old November 6th, 2009, 03:21 PM
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Quote:
Originally Posted by Liselle View Post
2x^2 - 3x - 5 = 0
I'm lost as to how I get rid of the 2 in 2x^2 so that it's x^2. I keep getting fractions that have very high LCDs.
Who told you you had to get rid of the 2 ?
2x^2 - 3x - 5 = (2x - 5)(x + 1)

Go here to learn: algebra.help -- Factoring A Trinomial
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Old November 6th, 2009, 03:28 PM
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You cannot get rid of it (unless dividing everything by 2 but then it gets tricky). But you can still factorize this equation :

2x^2 - 3x - 5 = (x + 1)(2x - 5)

But I agree, it is not always obvious to factorize such equations. Have you learnt the quadratic formula yet ? It always works and even tells you when no factorization is possible instead of letting you struggle with an unsolvable problem in R. Here is a spoiler, if you want to know about it :

Spoiler:
Quadratic formula (I won't put the details, they are found on Wiki) :

Say : ax^2 + bx + c = 0

You can define a "discriminant" (to know where it comes from, wikipedia) : \triangle = b^2 - 4ac

If this discriminant is negative, then the equation has no solution in R and cannot be factorized (you'll see later it has solutions, though).
If this discriminant is zero, then the equation has one root (solution). In fact, it has two, but they are the same. This solution is :

x = \frac{\ {-b}}{2a}

If this discriminant is positive, then the equation has two distinct roots :

x = \frac{\ {-b} {\pm} \sqrt{\triangle}}{2a}

There you go

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Old November 6th, 2009, 04:27 PM
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you cannot get rid of the 2, unless you divided the whole equation by 2 which would make the quadratic more difficult. simply factorise the equation:
2x2-3x-5=0
(2x-5)(x+1)=0
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Old November 6th, 2009, 04:59 PM
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For this equation factoring isn't too difficult but because I'm lazy I nearly always use the quadratic formula
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