Question

Factor the polynomials comletely, then solve 9x^2 +66x+21 = 0​

Answer 1

Answer:

x= -1/3

x = -7

Step-by-step explanation:

9x^2 +66x+21 = 0​

a=9 b=66 c=21

quadratic formula

x=(-b +/- square root of (b^2 – 4ac))/(2a)

x = (-66 +/- square root of (66^2 -4*9*21))/(2*9)

x = (-66 +/- square root of (4356 -756))/(18)

x = (-66 +/- square root of (3600))/(18)

x = (-66 +/- 60)/18

split the fraction

(-66 +/- 60)/18 = -6/18 and -126/18 because of the +/-

x = -6/18  x = -126/18

x = -1/3   x = -7

Answer 2

$~~~~~~9x^2+66x+21 = 0\\\\\implies 3(3x^2+22x+7)=0\\\\\implies 3x^2+22x+7=0\\\\\implies 3x^2 +21x +x +7=0\\\\\implies 3x(x+7) +(x+7)=0\\\\\implies (x+7)(3x+1)=0\\\\\implies x = -7~~ \text{or}~~ x =-\dfrac 13$