solving quadratic equations by factoring

Question

Use the zero product property to find the solutions to the equation (x + 2) (x + 3) = 12.

Answer 1

As an alternative method, this solution uses the quadratic formula (Chaoyun L has illustrated the factoring method in her solution):

 

x²+5x+6=12.......expand left hand side

x²+5x-6=0..........subtract 12 from both sides

 

Now use the quadratic formula to solve for "x"......

 

      -b±√(b²-4ac)
r= -----------------
              2a

 

where a=1, b=5, c=-6

 

x=(-5±√(5²-4(1)(-6))) / (2(1))...substitutes values for "a, b, c"

  =(-5±√(25+24)) / 2

  =(-5±√49)/2

  =(-5±7)/2............calculate both roots, pos and neg radical values

x=(-5+7)/2=2/2=1

             -or-

x=(-5-7)/2=-12/2=-6

 

So the solutions are x=1, -6 for the given equation.

 

Now plug these values into the original equation from the prob 

statement and check for truth (i.e. 12=12).  Always check your 

work, solution.

 

 

Answer 2

(x + 2) (x + 3) = 12

x²+5x+6=12

x²+5x+6-12=0

x²+5x-6⁼⁰

(x+6)(x-1)=0

x=-6 or =1