# Thread: Quadratic eq., solve for x when first variable is not 1

1. ## Quadratic eq., solve for x when first variable is not 1

$\displaystyle 2x^2 - 3x - 5 = 0$

I'm lost as to how I get rid of the 2 in $\displaystyle 2x^2$ so that it's $\displaystyle x^2$. I keep getting fractions that have very high LCDs.

2. hello
$\displaystyle 2x^2-3x-5 =(x+1)(2x-5)$

3. Originally Posted by Liselle
$\displaystyle 2x^2 - 3x - 5 = 0$
I'm lost as to how I get rid of the 2 in $\displaystyle 2x^2$ so that it's $\displaystyle x^2$. 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

You cannot get rid of it (unless dividing everything by $\displaystyle 2$ but then it gets tricky). But you can still factorize this equation :

$\displaystyle 2x^2 - 3x - 5 = (x + 1)(2x - 5)$

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 : $\displaystyle ax^2 + bx + c = 0$

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

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 :

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

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

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

There you go

5. 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

6. For this equation factoring isn't too difficult but because I'm lazy I nearly always use the quadratic formula