Verified Answer :

\(The\ zeros\ of\ a\ function\ f(x)\ is\ when\ f(x)=0.\\------------------------\\f(x)=(x+2)^2-25\\the\ zeros,\ if\ f(x)=0\iff(x+2)^2-25=0\\\\(x+2)^2-5^2=0\ \ \ \ |use\ a^2-b^2=(a-b)(a+b)\\\\(x+2-5)(x+2+5)=0\\\\(x-3)(x+7)=0\iff x-3=0\ or\ x+7=0\\\\x-3=0\ \ \ |add\ 3\ to\ both\ sides\\\boxed{x=3}\\or\\x+7=0\ \ \ \ \ |subtract\ 7\ from\ both\ sides\\\boxed{x=-7}\\\\Answer:\boxed{(4)\ -7\ and\ 3}\)

f(x) = 0

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1) 

İf    x=-2,

\(f(-2) = ((-2) + 2 ) ^{2} -25 = 0-25 = -25\)

f(x) ≠ 0

If   x= 5

\(f(5) = (5+2)^{2} - 25 = 49 - 25 = 24\)

f(x) ≠ 0
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2)  

If  x= -3

\(f(-3) = ((-3) + 2) ^{2} - 25 = 1 -25 =-24\)

f(x) ≠ 0

If  x= 7

\(f(7) = (7+2)^{2} - 25 = 81 - 25 = 56\)

f(x) ≠ 0

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3)

If  x= -5

\(f(-5) = ((-5)+2)^{2} - 25 = 9-25 = -16\)

f(x) ≠ 0

If  x= 2

\(f(2) = (2+2)^{2} - 25 = 16-25 = -9\)

f(x) ≠ 0
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4) 

If  x= -7

\(f(-7) = ((-7) +2 )^{2} - 25 = 25-25 =0\)

\(f(x) =0\)  ✔

If  x= 3

\(f(3) = (3+2)^{2} - 25 = 25-25 =0\)

\(f(x) =0\)  ✔

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Answer: 4

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