Which of the following are solutions to the equation below 6x-2x+36=5x^2+10x

Two real solutions

x =(6-√756)/-10=3/-5+3/5√ 21 = 2.150

x =(6+√756)/-10=3/-5-3/5√ 21 = -3.350

Step-by-step explanation:

Solve Quadratic Equation using the Quadratic Formula

4.3     Solving    -5x2-6x+36 = 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   =     -5

                     B   =    -6

                     C   =   36

Accordingly,  B2  -  4AC   =

                    36 - (-720) =

                    756

Applying the quadratic formula :

              6 ± √ 756

  x  =    —————

                   -10

Can  √ 756 be simplified ?

Yes!   The prime factorization of  756   is

  2•2•3•3•3•7

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).

√ 756   =  √ 2•2•3•3•3•7   =2•3•√ 21   =

               ±  6 • √ 21

 √ 21   , rounded to 4 decimal digits, is   4.5826

So now we are looking at:

          x  =  ( 6 ± 6 •  4.583 ) / -10

Two real solutions:

x =(6+√756)/-10=3/-5-3/5√ 21 = -3.350

or:

x =(6-√756)/-10=3/-5+3/5√ 21 = 2.150

Two solutions were found :

x =(6-√756)/-10=3/-5+3/5√ 21 = 2.150

x =(6+√756)/-10=3/-5-3/5√ 21 = -3.350

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