9x^2+42x+49=?

9x^2+42x+49=
9x^2+21x+21x+49= taking two number such that their sum is 42 and product is 441(49*9)
3x(3x+7)+7(3x+7)=
(3x+7)(3x+7)=
(3x+7)^2

9x^2 + 42x + 49
= (3x + 7)(3x + 7)
= (3x + 7)^2

This is a perfect square trinomial A^2 + 2AB + B^2 and it can be factored into (A+B)(A+B) or (A+B)^2.

9x^2+42x+49 = (3x)^2 + 2(3x)(7) + 7^2
In this case A = 3x and B = 7.

Therefore, 9x^2+42x+49 = (3x+7)^2

9x^2+42x+49
=9(x^2+42/9x+(42/18)^2-(42/18)^2)+49
=9(x+42/18)^2-42*42/18*18*9+49
=9(x+42/18)^2-119+49
=9(x+42/18)^2-70

9x^2+42x+49=
9x^2+21x+21x+49= taking two number such that their sum is 42 and product is 441(49*9)
3x(3x+7)+7(3x+7)=
(3x+7)(3x+7)=
(3x+7)^2

9x^2+42x+49=?

What do you want to know? Go on assigning numerical values to x and you will get infinite number of solutions.

(3x+7)(3x+7)
x=-7/3

9x²+42x + 49 = 0
(3x + 7)(3x + 7 ) = 0

x = -7/3