4questions 90 points

1. what are the solutions to the equation?
n^2 − 8n + 16=25

2. solve for b.
c = b^2/25

3. solve for t.
d = −16t^2 + 12t

4. what are the solutions to the equation?
5w^2 + 10w = 40

1  n=9   n=-1

2.  ±5 sqrt(C) =b

3. 3/8 ±1/8 sqrt(9-4d) = t

4.  w = 4 or -2

Step-by-step 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

5050

hope this !