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

because they could drop even lower..

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b