Question

Solve this quadratic equation by factorisation
2x²+x-300=0

Answer 1

Answer:

x = -25/2 = -12.500 pls look down for explanation.

Step-by-step explanation:

The first term is,  2x2  its coefficient is  2 .

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

The last term, "the constant", is  -300  

Step-1 : Multiply the coefficient of the first term by the constant   2 • -300 = -600  

Step-2 : Find two factors of  -600  whose sum equals the coefficient of the middle term, which is   1 .

     -600    +    1    =    -599  

     -300    +    2    =    -298  

     -200    +    3    =    -197  

     -150    +    4    =    -146  

     -120    +    5    =    -115  

     -100    +    6    =    -94  

     -75    +    8    =    -67  

     -60    +    10    =    -50  

     -50    +    12    =    -38  

     -40    +    15    =    -25  

     -30    +    20    =    -10  

     -25    +    24    =    -1  

     -24    +    25    =    1    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -24  and  25  

                    2x2 - 24x + 25x - 300

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

                   2x • (x-12)

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

                   25 • (x-12)

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

                  (2x+25)  •  (x-12)

Answer 2

Step-by-step explanation:

$= {2x}^{2} + x - 300 \\ = {2x}^{2} + (25 - 24) x - 300 \\ = {2x}^{2} + 25x - 24x - 300 \\ = x(2x + 25) - 12(2x + 25) \\ = (2x + 25) (x - 12)$

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