Question

What are the roots of the equation 2x^2+x=6​

Answer 1

Answer:

(2x - 3)(x + 2)

Step-by-step explanation:

Step  1  :

Equation at the end of step  1  :

 ($2x^{2}$ +  x) -  6

Step  2  :

Trying to factor by splitting the middle term

2.1     Factoring  $2x^{2}$+x-6

The first term is,  $2x^{2}$  its coefficient is  2 .

The middle term is,  +x  its coefficient is  1 .

The last term, "the constant", is  -6

Step-1 : Multiply the coefficient of the first term by the constant   2 • -6 = -12

Step-2 : Find two factors of  -12  whose sum equals the coefficient of the middle term, which is   1 .

     -12    +    1    =    -11

     -6    +    2    =    -4

     -4    +    3    =    -1

     -3    +    4    =    1    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -3  and  4

                    $2x^{2}$ - 3x + 4x - 6

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (2x-3)

             Add up the last 2 terms, pulling out common factors :

                   2 • (2x-3)

Step-5 : Add up the four terms of step 4 :

                   (x+2)  •  (2x-3)

            Which is the desired factorization

(2x - 3)(x + 2)