Question

quadratic equation x²-24x-25​

Answer 1

Answer:

Solving    x2-24x-25 = 0 by the Quadratic Formula .

 According to the Quadratic Formula,  x  , the solution for   Ax2+Bx+C  = 0  , where  A, B  and  C  are numbers, often called coefficients, is given by :

                                     

            - B  ±  √ B2-4AC

  x =   ————————

                      2A 

  In our case,  A   =     1

                      B   =   -24

                      C   =  -25 

Accordingly,  B2  -  4AC   =

                     576 - (-100) =

                     676

Applying the quadratic formula :

               24 ± √ 676 

   x  =    ——————

                      2

Can  √ 676 be simplified ?

Yes!   The prime factorization of  676   is

   2•2•13•13  

To be able to remove something from under the radical, there have to be  2  instances of it (because we are taking a square i.e. second root).

√ 676   =  √ 2•2•13•13   =2•13•√ 1   =

                ±  26 • √ 1   =

                ±  26 

So now we are looking at:

           x  =  ( 24 ± 26) / 2

Two real solutions:

x =(24+√676)/2=12+13= 25.000 

or:

x =(24-√676)/2=12-13= -1.000