1. ## How do i solve this? (quadratics)

How do I solve this?

Determine the point(s) of intersection of the following two parabolas

f(x)= x^2 -10x + 21 and g(x)= -x^2 + 12x -35

(i did this: x^2 -10x + 21 = -x^2 + 12x -35 and then i added them all, changing the signs of the second expression because thats how i was tought, and i got this 2x^2 -22x +56 and after that i am supposed to find two numbers that multiplied give me 56 and added -22... but i think i got it all wrong, im so confused!!!! help!)

2. Originally Posted by MonaMath
How do I solve this?

Determine the point(s) of intersection of the following two parabolas

f(x)= x^2 -10x + 21 and g(x)= -x^2 + 12x -35

(i did this: x^2 -10x + 21 = -x^2 + 12x -35 and then i added them all, changing the signs of the second expression because thats how i was tought, and i got this 2x^2 -22x +56 and after that i am supposed to find two numbers that multiplied give me 56 and added -22... but i think i got it all wrong, im so confused!!!! help!)
From $x^2 -10x + 21 = -x^2 + 12x -35$ you'll get:

$2x^2 -22x +56=0~\implies~2(x^2-11x+28)=0$

Try to factorize the term in brackets. Keep in mind that the divisors of 28 are 1, 2, 4, 7, 14, 28.