SOLUTION: How would you solve this quadratic equation 5x squared

SOLUTION: How would you solve this quadratic equation 5x squared - 8x +3=0

Question 2153: How would you solve this quadratic equation 5x squared - 8x +3=0
Answer by longjonsilver(2297) (Show Source): You can put this solution on YOUR website!
you would hope it factorised firstly. If you could not see the factors, you would have to resort to "completing the square" or the "number crunching" version of this...the Quadratic formula.
For factorising...always the simplest solution and "good fun". Well, OK, not good fun, but certainly "enjoyable". Well, OK, not enjoyable...lol i digress with some English humour, sorry :-D
Factorising...we want 2 things multiplied together...()()=0. These will both have an x term and a pure number term, in general (x+a)(x+b), which expands to give x^2 + (a+b)x + ab. Your equation is lightly more complicated in that you have a 5 factor too!
so...2 "x" terms that give 5x^2?...take the obvious...5x and x. Voila. First guess done, so we have (5x)(x)=0
Now for the a and b terms!. Look at the general equation...the a and b multiply to give ab and then also add to give the coefficient of the x term. So basic numbers for you. As you Americans would say...4th grade stuff (or whatever)...
Your equation is more tricky in one sense, but because of that, it is easier n another sense...
which 2 number multiply to give +3
and also add together to give -8.
Well?
the answer we need is ONLY 1x3 works easily for us, so let's hope these are the answers!!!. This is approach i use to this day, so do not feel it is a cop-out to work like this.
So either (5x-1)(x-3) or (5x-3)(x-1) is the answer, i hope.
The first answer when multiplied out will give the following terms...-15x and -3x..no way is this -8x, so WRONG WRONG WRONG!!!!
Second answer? well this will give -5x and -3x which is -8x. YIPPPEEEEE, the answer...
(5x-3)(x-1)=0
hence 5x-3=0 OR x-1=0
so
x=3/5, x=1
jon
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