how to solve this?

Question

Solve the equation.


y²=5y+36

Answer 1

Hi Jay,

 

  Solve the equation.


y²=5y+36

 

 

This a quadratic equation.  To solve it all the terms must be on the same side.

So add -5y+36 to both sides.

 

y²-5y+36=0

 

 

This is not factorable.  So, we need to use the quadratic formula.

 

a=1

b=-5

c=36

 

x=-b±√(b²-4ac)

    --------------

          2a

 

x=-(-5)±√((-5)²-4(1)(36)

   ------------------------

            2(1)

 

simplifying

 

x=5±√(25-144)

    --------------

           2

 

x=5±√(-119)

   ------------

           2

 

The √(-1)=i which is an imaginary number.  So the √(-119)=i√(119)

there is not a perfect square in the  √119 so it can not be further simplified.

 

ANSWER:  

 

x=5+i√(119)         and x=5-i√(119)
     ----------                   ----------
         2                                  2

 

 

We're finished!