Answer:
-13,1
Step-by-step explanation:
f(x)= (x+6)^2-49
When we find the zero's we set f(x) =0
0= (x+6)^2-49
Add 49 to each side
49= (x+6)^2-49+49
49= (x+6)^2
Take the square root of each side
±sqrt(49) = sqrt((x+6)^2)
±7 = (x+6)
Subtract 6 from each side
±7-6 = (x+6-6)
±7-6 = x
7-6 =x -7-6 =x
1=x -13=x
Answer:
x = -13 or x = 1
Step-by-step explanation:
(x+6)^2 is x^2+12x+36
(x+6)^2-49 is x^2+12x-13, looks hard to factor.
BUT (x+6)^2 - 49 is the difference of two squares, so the factorization is
(x+6+7)(x+6-7) = (x+13)(x-1),
which is factorization of x^2+12x-13.
The expression is zero when either factor is zero, x = -13 or x = 1
Check: f(x) = (x+6)^2-49
f(-13) = (-13+6)^2-49 = (-7)^2-49 = 0
f(1) = (1+6)^2-49 = (7)^2-49 = 0
