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embizze eNotes educator| Certified Educator

Solve `2x^2+3x=2` :

First write in standard form:


I. You can use a guess and check strategy: you know the factored form will be of the form (a+b)(c+d). So ac=`2x^2` ; the only way to get that is `(2x+b)(x+d)` . Now bd=-2 and there are four ways to do that:





Checking using the distributive property (FOIL) we see that the second is thecorrect one:

`(2x-1)(x+2)=0` Using the zero product property we get:

`2x-1=0`  or `x+2=0` So

`x=1/2` or -2

(2) Another method: `2x^2+3x-2=0`

Let M=2(-2)=-4 (Mulitply the leading coefficient and the constant term)

We need a p and q such that pq=-4 and p+q=3 (The product of p and q is M, while the sum of p and q is the linear term)

We find p=4 and q=-1to work. (You could also use p=-1,q=4)

Rewrite `2x^2+3x-2` as `2x^2+4x-1x-2` ; now factor 2 terms at a time, taking out the common factor:

`2x^2+4x-1x-2=2x(x+2)-1(x+2)=(2x-1)(x+2)` so:



The solution is `x=1/2` or `x=-2` :





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