Solve for f.

(f - 12)2 = 25

A. f = 5 or f = −5

B. f = 12 or f = −12

C. f = 17 or f = 7

D. no solution

Multiply to get rid of the parenthesis.

2f - 24 = 25

Add 24 to both sides.

2f = 49

Divide both sides by 2.

f = 28.5

Unless you have a typo somewhere, none of the alternatives fit.

Looks like he meant

(f-12)^2 = 25
so,
f-12 = ±5
f = 12±5
f = 17 or 7

To solve for f in the equation (f - 12)2 = 25, we can start by expanding the equation:

(f - 12)2 = 25
f2 - 24f + 144 = 25

Now, let's simplify the equation by moving all the terms to one side:

f2 - 24f + 119 = 0

To solve this quadratic equation, we can use the quadratic formula:

f = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 1, b = -24, and c = 119. Plugging in these values, we get:

f = (-(-24) ± √((-24)^2 - 4(1)(119))) / (2(1))
f = (24 ± √(576 - 476)) / 2
f = (24 ± √100) / 2
f = (24 ± 10) / 2

Now we have two possible solutions:

f1 = (24 + 10) / 2 = 34 / 2 = 17
f2 = (24 - 10) / 2 = 14 / 2 = 7

Therefore, the solutions to the equation (f - 12)2 = 25 are f = 17 or f = 7. Therefore, the correct answer is C. f = 17 or f = 7.