Solve 2x^2 - x - 21 by factorising
Lets begin by splitting the bx term to make factorising possible: 2x2 - x - 21 is the same as 2x2 - 1x - 21What two numbers = -1 when added, and = -42 when multiplied together?(note - they have to multiply to -42 and not -21, because the equation begins for 2x2 , not x2 , and we account for the 2 by multiplying it with the c term)Answer: 6 and -7 !Insert this into the equation: 2x2 +6x - 7x - 21We can now begin to factorise! What is the highest common factor between 2x2 +6x?Answer: 2xWhen factorising these terms, you should get 2x(x+3)The remaining terms are - 7x - 21What is the highest common factor?Answer: -7When factorising these terms, you should get -7(x+3)Combine the two halves together again, and you should get:2x(x+3) -7(x+3)This can be rewritten as (2x-7)(x+3) - now you have factorised the equation!To solve:Let x+3 = 0Therefore x= -3OrLet 2x-7 = 0so 2x=7Therefore x=7/2FINAL ANSWER: x = -3 , x = 7/2 - This is because BOTH ANSWERS ARE CORRECT - quadratic equations usually have 2 solutions!
