8x^2+20x-9=0

Question

need to write in general form

Answer 1

We can do this by completing the square....(x+p)^2 +q =0

 

 

 

 

1) add your 9 to both sides, starting out you only want x's on the left. -- > 8x^2+20x = 9

 

2) now you only want it to be x squared, no coefficient. Divide everything by 8 --> x^2 + 20x/8 = 9/8.

 

3) lets reduce fractions --> x^2 + 5x/2 = 9/8.

 

 

 

 

4) this is the important part b/c we are completing the square and we need to make it look like (x+p)^2

... the 5x/2, i want to take the coefficient and divide it by 2, then square it.  if you have a ti 83/89/84 or some graphing calculator that most high school kids use, just hit (5/2)/2 enter, then hit the x^2 button to square it, then hit math, enter, enter to make it back into a fraction.  if you did that correctly, you should have 25/16

 

I want to take that 25/16 and add it to both side of our equation.

-->  x^2 + 5x/2 + 25/16 = 9/8 + 25/16      or  x^2 + 5x/2 + 25/16 = 43/16

 

 

5) Second to last step, parabolas are usually ax^2 +bx + c.  At this stage of the game when you complete the square, take the square root of the a term (in our case its just 1) and take the square root of the c term (25/16).  If you take the square root of 25/16 you get 5/4.  These are the terms we are going to put under the parenthesis in the general form.  (x+5/4)^2 = 43/16.       (x + 5/4)^2 is actually the factored form of  x^2 + 5x/2 + 25/16.

 

6) Last step---- subtract 43/16 on both sides

 

--> (x+5/4)^2 - 43/16 =0 and you are done : )

 

 

 

 

 

 

!!!!Shortcut!!!!!

parabolas are y = ax^2 + bx +c

 

 

general form will be y= (x+b/2a)^2 + (c/a) - (b^2/4a^2)

Answer 2

 

   8 X² + 20X - 9 = 0

 

     List facors 0f 72(8*9) = 2 * 2 * 2* 3 * 3 = 2*36 = 4*18 = 2* 36

    

     The difference of None of its factors is 20

 

      Therefore it is not facorable

 

  Have to use quadratic formula to find out the roots:

 

      X_1, X_{2 =  -20/16 ±}  √(20² +288)   = -5/4 ± √688 = -5/4 ±√43

                                     16                             16