Solve the equation x^2-10x+21=0

First of all notice the highest power on this equation is '2' so it must be a quadratic equation. Using the general form Ax^2+Bx+C=0 we must find two numbers that are factors of C and add together to get B. Now apply this to the question, we must find two factors of 21 that add up to get -10, the factors of 21 are 1 & 21 which is obvious they do not add to get -10,7 & 3 also are factors to get 21 but do not add to get -10 again. Now by using the sign of C we can recognition a pattern with the two numbers, this is when C is positive the two factors are the same sign, and when C is negative the two factors are different signs. We have tried 7 & 3, now we can try -7 & -3 which does add up to -10, Therefore we have found the correct two numbers to factorize this expression. Remember factorize means put in brackets so the equation x^2-10x+21=0 is equal to (x-7)(x-3)=0 . This equation means (x-7)=0 or (x-3)=0 so by making x the subject (assuming knowledge of making x the subject) x=7 or x=3. We can sub these values into the original equation to see (7)^2-10(7)+21=0 or (3)^2-10(3)+21=0 and we have now solved the equation x^2-10x+21=0.