Explanation:
Solve 2x^2-11x+14=0 give me 2 ways to get the 2 values of x?
The first way is to make factors by middle-term splitting. You get (x-2)(2x-7)=0, so the solution is x=2,7/2.
The other way is to use the formula for the solution of roots. Roots= (-b+ rootD)/2a, (-b-rootD)/2a, if the equation is of the form ax^2+bx+c=0. Here D is the discriminant. D=b^2-4ac
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Lets assume your equation is of the form ax^2+ bx + c =0
First method :
By breaking 'b' factor of x into two parts using factors of 'ac' ( a *c)
like 2* 14 = 28 = 7* 4 ( b is 11 which could be splitted in values 7 and 4)
equation becomes 2x^2 -4x-7x+14 = 0
take out common factors 2x(x-2) -7 (x-2) = 0
which is (2x-7) (x-2) =0 ; x =2,7/2 are two values
Second method:
make equation in the form of (x+h)^ 2 - k = 0 ; then x+h = +sqrt(k) and -sqrt(k)
which will give x as -h+sqrt(k) , +sqrt(k)
2x^2 - 11x +14 =0 wil become x^2 -11/2 x + 7 = 0
which is (x-11/4)^2 + 7- 121/16 =0
(x-11/4)^2 = (121/16) - 7 = 9/16
x- 11/4 = 3/4 and -3/4
x = 14/4 and 8/4 = 7/2 and 2