3.) t² + 4t - 14=0
4.) 25 - 4f²=0
5.) (q+2)²- 36=0
6.) x² + 6x - 4=0
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3.) t² + 4t - 14=0
4.) 25 - 4f²=0
5.) (q+2)²- 36=0
6.) x² + 6x - 4=0
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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