Answer:
1 n=9 n=-1
2. ±5 sqrt(C) =b
3. 3/8 ±1/8 sqrt(9-4d) = t
4. w = 4 or -2
Explanation:
1 n^2 − 8n + 16=25
Subtract 25 from each side
n^2 − 8n + 16-25=25-25
n^2 − 8n -9 =0
Factor
What two numbers multiply to negative 9 and add to -8
-9*1 = -9
-9+1 = -8
(n-9) (n+1) =0
Using the zero product property
n-9= 0 n+1 = 0
n-9+9 =0+9 n+1-1 = 0-1
n=9 n=-1
2. C = b^2/25
Multiply each side by 25
25C = b^2/25*25
25C = b^2
Take the square root of each side
±sqrt(25C) = sqrt(b^2)
±sqrt(25C) = b
±sqrt(25) sqrt(C) =b
±5 sqrt(C) =b
3. d = −16t^2 + 12t
Factor out -16 from the right side
d = -16(t^2 -12/16 t)
Divide by -16
d/-16 = -16/-16 (t^2 -12/16 t)
-d/16 = (t^2 -3/4 t)
Completing the square
we need to add (-3/4 ÷2) ^2 to each side = (-3/8)^2 = 9/64
-d/16 +9/64 = (t^2 -3/4 t + 9/64)
Get a common denominator
-4d/64 + 9/64 = (t-3/8)^2
(9-4d)/64 = (t-3/8)^2
Take the square root of each side
±sqrt((9-4d)/64 ) =sqrt (t-3/8)^2
±sqrt((9-4d)/64 ) = (t-3/8)
±sqrt(9-4d)/ sqrt(64 ) = (t-3/8)
±1/8 sqrt(9-4d) = (t-3/8)
Add 3/8 to each side
3/8 ±1/8 sqrt(9-4d) = (t-3/8)+3/8
3/8 ±1/8 sqrt(9-4d) = t
4. 5w^2 + 10w = 40
Divide by 5
5/5w^2 + 10/5w = 40/5
w^2 +2w=8
Complete the square by adding (2/2)^2 to each side = 1
w^2 +2w +1 = 8+1
w^2 +2w+1 = 9
(w+1)^2 = 9
Take the square root of each side
sqrt((w+1)^2) = ±sqrt(9)
(w+1) = ±3
Subtract 1 from each side
w+1-1 = ±3-1
w = ±3-1
w = 3+1 or -3+1
w = 4 or -2