Answer:
C x = (-5+sqrt(-3))/2
D x = ( -5-sqrt(-3))/2
Step-by-step explanation:
Set the polynomial equal to zero
x^2 + 5x+7 =0
Subtract 7 from each side
x^2 + 5x+7-7 =-7
x^2 + 5x = -7
Complete the square by taking the coefficient of x and dividing by 2 and then squaring it
(5/2)^2 = 25/4
x^2 + 5x + 25/4 = -7+25/4
(x+5/2)^2 = -28/4 +25/4
(x+5/2)^2 = -3/4
Take the square root of each side
x+5/2 = ±sqrt(-3/4)
Subtract 5/2 from each side
x+5/2 -5/2 = -5/2±sqrt(-3/4)
x = -5/2±sqrt(-3/4)
x = -5/2±sqrt(-3)/2
x = (-5±sqrt(-3))/2
