x squared - 7x +10 = 0?

(x-5)(x-2)=0
x=5 and 2

List all number combinations that multiply to get 10:
1, 10
2, 5
-1, -10
-2, -5

Now add these together to find which combination equals -7:

1 + 10 = 11 NO
2 + 5 = 7 NO
-1 + -10 = -11 NO
-2 + -5 = -7 YES


(x-2) (x-5)=0

x = 2, 5

x^2 - 7x + 10 = 0
x^2 - 5x - 2x + 10 = 0
(x - 5)(x - 2) = 0

x - 5 = 0
x = 5

x - 2 = 0
x = 2

∴ x = 5 , 2

(x - 5)(x - 2) = 0
x = 2 , x = 5

x^2 - 7x + 10
=(x-2)(x-5) (i factorised it in my mind)
(x-2)(x-5)=0
x-2=0 or x-5=0
x=2 or 5
(how i factorised it mentally?skill in addition and multiplication)

this is in the form of ax^2 + bx + c = 0
here with x^2 - 7x + 10 = 0 you will have the followings:
a=+1, b=-7, c=+10
Delta = b^2 - 4ac = (-7)^2 - 4*(+1)*(+10) = 9
So x1= [-b+ squared root of Delta]/2a = [-(-7) + squared root of 9]/(2*1)=5
x2= [-b- squared root of Delta]/2a= [-(-7)-squared root of 9]/(2*1)=2

So you have to value of x: 5 and 2

If we have the quadratic equation ax²+bx+c=0
Here we have a=1 b=-7 c=10
Then the roots are computed from the type:
x=(-b±√(b²-4ac))/(2a)
If you solve you will find :
x1=5 and x2=2

x^2 - 7x +10 = 0 = (x - 5 ) (x - 2 ) so x =5, 2 are solutions