The correct option C and F
Step-by-step explanation:
x² + 6x = 16
we need to check the other options to find out its equivalence.
a) x² + 6x + 9 = 0
Rewritting the equation above: x² + 6x - 16 = 0
From the above, we can see they are different
b) x² + 6x + 9 = 16
rewritting: x² + 6x + 9 - 16 = 0
x² + 6x - 7 = 0
This is not equivalent to x² + 6x - 16 = 0
c) x² + 6x + 9 = 25
x² + 6x + 9 -25 = 0
x² + 6x -16 = 0
x² + 6x = 16
This is equivalent to x² + 6x = 16
d) (x + 3)² = 0
(x+3)(x+3) = 0
x(x+3)+3(x+3) = 0
x² +3x +3x + 9 = 0
x² + 6x + 9 = 0
This is not equivalent to x² + 6x - 16 = 0
e) (x+3)² = 16
(x+3)(x+3) = 16
x(x+3)+3(x+3) = 16
x² +3x +3x + 9 = 16
x² + 6x + 9 = 16
x² + 6x = 16 - 9
x² + 6x = 7
This is not equivalent to x² + 6x - 16 = 0
f) (x+3)² = 25
(x+3)(x+3) = 25
x(x+3)+3(x+3) = 25
x² +3x +3x + 9 = 25
x² + 6x + 9 = 25
x² + 6x = 25 - 9
x² + 6x = 16
This is equivalent to x² + 6x = 16
The correct option C and FF
x(x+3)+3(x+3) = 16
x² +3x +3x + 9 = 16
x² + 6x + 9 = 0