@dan815
Can you help me out? I am trying to solve this quadratic equation by using any method (I used the quadratic formula) and I can't get it right. Here it is, 3x^2 +7=22x

And I rewrote it to equal, 3x^2 -22x +7. Can you show me how to solve this (it recommends factoring but I have been terrible so far in problems like this with a number in front of the x2.

Question

@dan815 
Can you help me out? I am trying to solve this quadratic equation by using any method (I used the quadratic formula) and I can't get it right. Here it is, 3x^2 +7=22x

And I rewrote it to equal, 3x^2 -22x +7. Can you show me how to solve this (it recommends factoring but I have been terrible so far in problems like this with a number in front of the x2.

anonymous · Answer

I got it to (x- ?/3) and (x+ ?/3) but can't find an answer

retireed · Answer

3x^2 -22x +7

These days they teach factoring a lot better than they did when I was young.  They seem to want you to look for factors (this might not the right word)   of "b" coefficient that might work.

In this case,  B = 22 ,  so 1 and 22, 
                                       2 and 11     
when multiplied together = 22.  That works best  when "a" is 1

For this equation I see 3 times 7 equals 21 plus one equals 22.  I know it is confusing, but bear with me.

     How can I get 21 + 1 to equal -22    

Read this and think about and I will explain.  Answer to follow

retireed · Answer

Are you still there?

anonymous · Answer

Yes

retireed · Answer

Let's see here....
    3 * -7   plus 1 * -1   add up to -22   also a big clue the "c" coefficient is +7    
so
     ( _x - __ ) ( _x - __ )

     ( _x - 1 ) ( _x - 7 )     -1 * -7  insures c will equal +7

What  __x  * ___x     will cause the "a" to equal +3 ????   Fill in the blanks.

anonymous · Answer

3 and 1?

retireed · Answer

YES!

Now which one goes where?   

Remember we need the "b" to equal -22

anonymous · Answer

The 1 would go with the 7 and the 3 with the 1?

retireed · Answer

Copy this ....

   ( _x - 1 ) ( _x - 7 )

and replace the blank with the number, so I know that you understand.  I think you got it right, but I'm not sure.

anonymous · Answer

I did to get (3x-1) (1x-7). So when I enter my answer it should be 1/3, and 7.

anonymous · Answer

would that be the answer?

retireed · Answer

That looks great.   The 1/3 and 7 will be the roots or the values of x that cause the y to equal zero.

anonymous · Answer

I'll enter it and see what I get...

anonymous · Answer

CORRECT!  Thanks so much! So the point of the problem is to find hat factor that equals b but when reduced with equal c?

retireed · Answer

That sounds close, somehow 'a' and 'c' combined must sum to 'b'

anonymous · Answer

ok. Thank you!

retireed · Answer

Anytime.