I need assistance in solving a quadratic equation

Algebra
Tutor: None Selected Time limit: 1 Day

   

I am stuck on the factoring, I can not find a combination of numbers that work here, please help!

Apr 5th, 2015

I can help you with this.

First write out all the factors for the first and the last term in the equation.  Then you need to look for a combination that will add or subtract to equal the middle number.

Not all equations can be factored.  If you need to solve it there are other ways to do so.

To  be able to give a more detailed answer, please post the specific equation that you need factored.

Apr 5th, 2015

x^-3x+1=0

Apr 5th, 2015

I am assuming that you meant x^2 - 3x + 1 = 0.

If that is the case, then the equation cannot be factored.  The only factors for 1 are 1*1 or -1*-1 and the factors for x^2 would be x*x or -x*-x.  This combination can never be combined to give -3x.

Since you cannot factor this equation, the best way to solve would be to use the quadratic formula

x = { -(-3) +/- sqrt [ (-3)^2 - 4*1*1 ] } / 2*1

x = { 3 +/- sqrt [ 9 - 4 ] } / 2

x = { 3 +/- sqrt (5) } / 2

x = 2.618

x = 0.382

Apr 5th, 2015

If you cannot find the factors, it is most likely that the equation cannot be factored.  

You can also always use the quadratic equation to solve (unless the directions for the problem state other wise).

Apr 5th, 2015

Katrina, thank you so much for your help! Algebra is a very difficult subject for me so everything looks foreign. I am always unsure if something can be solved or not because usually I can not get my problems to work out, thank you for the clarification.   

Apr 5th, 2015

If you ever need to check for your self, using the quadratic formula can do that.  

If you would plug the number into the formula and get solution of whole numbers, then the equation could have been factored.  If you get decimals, like in the case above then the original problem could not be factored.

For example, if you had x^2 + 5x + 6 (Something that you would probably easily find the factors for), you could use the quadratic formula.

x = {-5 +/- sqrt ( 5^2 - 4*1*6) } / 2*1

x = -5 +/- sqrt ( 25 - 24) } / 2

x = -5 +/- sqrt ( 1 ) / 2

x = - 5 +/- 1 / 2

x = - 3

x = -2

This tells you that the original equation could have been factored as (x + 2)(x + 3) = 0

Apr 5th, 2015

Thank you for the great tips, I can understand it better now rather than reading it from a text I appreciate it very much, this is going into my notebook now!

Apr 5th, 2015

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