What is the solution set of x2 + 5x - 5 = 0?

x =(-5-√45)/2=(-5-3√ 5 )/2= -5.854

    x =(-5+√45)/2=(-5+3√ 5 )/2= 0.854

Step-by-step explanation:

2.3     Solving    x2+5x-5 = 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   =    5

                     C   =   -5

Accordingly,  B2  -  4AC   =

                    25 - (-20) =

                    45

Applying the quadratic formula :

              -5 ± √ 45

  x  =    —————

                   2

Can  √ 45 be simplified ?

Yes!   The prime factorization of  45   is

  3•3•5

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).

√ 45   =  √ 3•3•5   =

               ±  3 • √ 5

 √ 5   , rounded to 4 decimal digits, is   2.2361

So now we are looking at:

          x  =  ( -5 ± 3 •  2.236 ) / 2

Two real solutions:

x =(-5+√45)/2=(-5+3√ 5 )/2= 0.854

or:

x =(-5-√45)/2=(-5-3√ 5 )/2= -5.854

Two solutions were found :

    x =(-5-√45)/2=(-5-3√ 5 )/2= -5.854

    x =(-5+√45)/2=(-5+3√ 5 )/2= 0.854

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