Question 3457
I have these six problems that I need to work and can't remember what to do.

 1. x²-4=0 
  
Factor the LHS as the difference of two perfect squares
 
  (x-2)(x+2) = 0
   
Set each factor = 0

 x-2 = 0, or x = 2
 x+2 = 0, or x = -2

--------------------------------------------

2. x²+x=0


Factor the LHS by factoring out x
   x(x-2)

Set each factor = 0

    x=0,
    x-3 = 0, or x = 3

--------------------------------------------

3. x²+7x+12=0 

Factor the LHS by thinking of two positive integers that have product
12 and sum 7, they are 4 and 3.
 
  (x+4)(x+3) = 0
   
Set each factor = 0

 x+4 = 0, or x = 4
 x+3 = 0, or x = 3

-----------------------------------

4. x²+5x=-4

 Get 0 on the right by adding 4 to both sides:

   x²+5x+4 = 0

Factor the LHS by thinking of two positive intergers that have product
4 and sum 5, they are 4 and 1.
 
  (x+4)(x+3) = 0
   
Set each factor = 0

 x+4 = 0, or x = 4
 x+3 = 0, or x = 3

--------------------------------

 5. 3x²+5x-10=0 

That won't factor so you have to use the quadratic formula

   {{{(-b +- sqrt( b^2-4*a*c ))/(2*a) }}}

   {{{(-5 +- sqrt( 5^2-4*3*-10 ))/(2*3) }}}  
  
   {{{(-5 +- sqrt( 145))/6 }}}

---------------------------

6. 4x²+3x+8=0 

That won't factor so you have to use the quadratic formula

   {{{(-b +- sqrt( b^2-4*a*c ))/(2*a) }}}

   {{{(-5 +- sqrt( 3^2-4*4*8))/(2*4) }}}  
  
   {{{(-5 +- sqrt(-119))/8 }}}

That won't factor so you have to use the quadratic formula

   {{{(-b +- sqrt( b^2-4*a*c ))/(2*a) }}}

   {{{(-5 +- sqrt( 5^2-4*3*-10 ))/(2*3) }}}  

   {{{(-5 +- sqrt(-145))/6 }}}  

   {{{(-5 +- i*sqrt( 145))/6 }}}

Edwin