Welcome to Nur's Quadratic Equation Tutorial!



Goal: To be able to solve Quadratic equations by factoring and using the zero product property.


The equation x2 +bx+c is a trinomial. In order to solve the trinomial, factoring is necessary before it is possible to solve for x.
 


Example 1:  Factor x2 +6x-27 and solve for x.

  1. Goal: Make x2+6x-27 into a binomial [(x+m)(x+n)=0] in order to solve for x
  2. There are several ways to do this. I prefer to create an empty binomial and do it through the process of Guess and Check.
  3. (x+?)(x+?)=0
  4. Try to find numbers that have a product of -27 when multiplied, and equal 6 when multiplied.
  5. Some possible combinations are 9x-3, 3x-9, 27x1, etc.
  6. However, 9x(-3)=-27 AND 9+(-3)=6! Jackpot!!
  7. The binomial is (x+9)(x-3)=0
  8. But wait, we still need to solve for x!
  9. Use the zero product property to find x!
    1. (x+9)=0, x=-9 
    2. (x-3)=0, x=3
  10. If you solve for x, you will find that the answer for x2 +6x-27 is x=(-9) or x=3


Example 2:

       Sometimes x2 can have a coefficient.

Factor and solve for x: 2x2+9x-5

  1. The process is still the same: create an empty binomial, except this time, put 2 in one of them, because x2 has a number in front of it.
  2. Shown here: (2x+?)(x+?)
  3. Once again, look for numbers that equal -5 when multiplied (using FOIL in the binomial). Guess and check numbers, using FOIL each time to see if they prove right (if they turn out to be the exact trinomial)
  4. -1 and 5 work! Shown here: (2x-1)(x+5)=2x2+9x-5!!
  5. So if you solve for x using the zero product property again...
    1. 2x-1=0, x= 1/2
    2. x+5=0, x=-5
  6. Congratulations! You have solved for x!  The answer for 2x2+9x-5 is x=1/2 or x=(-5)

Now time for some... Practice Problems!!!

Factor and solve for x.

  1. x2+x-6=0

  2. x2+3x-10=0

  3. 2b2+7b+3=0

  4. x2+2x-15=0

  5. 2r2+5r=-3

  6. 25w2-16=0

  7. x2 + 5x + 6 = 0

  8. m2 – 3 = 2m.

  9. (g + 2)(g + 3) = 12 (Hint: It's not already factored for you!)