Answer:

3. t = -2 ± 3√2

4. f = 5/2

5. q = 4

6. -3 ± √13

Step-by-step explanation:

3. t^2 + 4t - 14 = 0

Completing the square:

t^2 + 4t = 14

t^2 + 4t + 4 = 14 + 4

t^2 + 4t + 4 = 18

Factor:

√(t + 2)^2 = √18

t + 2 = √18

t = -2 ± √18

t = -2 ± 3√2

4. 25 - 4f^2 = 0

-1*[-4f^2 = -25]

√4f^2 = √25

2f = 5

f = 5/2

5. (q+2)^2 = 36

√(q+2)^2 = √36

q+2 = 6

q = 4

6. x^2 + 6x - 4 = 0

Completing the square:

x^2 + 6x = 4

x^2 + 6x + 9 = 4 + 9

x^2 + 6x + 9 = 13

Factor:

√(x + 3)^2 = √13

x + 3 = √13

x = -3 ± √13