Use the quadratic formula to find the solutions (roots) of the equation x^2-10x-11=0

11,-1

Step-by-step explanation:

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Solve Quadratic Equation using the Quadratic Formula

3.3     Solving    x2-10x-11 = 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   =   -10

                     C   =  -11

Accordingly,  B2  -  4AC   =

                    100 - (-44) =

                    144

Applying the quadratic formula :

              10 ± √ 144

  x  =    —————

                   2

Can  √ 144 be simplified ?

Yes!   The prime factorization of  144   is

  2•2•2•2•3•3

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).

√ 144   =  √ 2•2•2•2•3•3   =2•2•3•√ 1   =

               ±  12 • √ 1   =

               ±  12

So now we are looking at:

          x  =  ( 10 ± 12) / 2

Two real solutions:

x =(10+√144)/2=5+6= 11.000

or:

x =(10-√144)/2=5-6= -1.000

Two solutions were found :

    x = 11

    x = -1