What is -16t^2+64t+80>50 ?

The solution to -16t^2+64t+80>50 is -(sqrt(47))/(2sqrt(2))+2<t<(sqrt(47))/(2sqrt(2))+2

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-16t^2+64t+80>50

- 16 t^{2} + 64 t + 80 > 50

- \frac{47}{2 2} + 2 < t < \frac{47}{2 2} + 2

Solution steps

- 16 t^{2} + 64 t + 80 > 50

Rewrite in standard form

- 8 t^{2} + 32 t + 15 > 0

Complete the square

- 8 t^{2} + 32 t + 15 : - 8 (t - 2)^{2} + 47

- 8 (t - 2)^{2} + 47 > 0

Move

47

to the right side

- 8 (t - 2)^{2} > - 47

Multiply both sides by

- 1

8 (t - 2)^{2} < 47

Divide both sides by

8

(t - 2)^{2} < \frac{47}{8}

For

u^{n} < a

, if

n

is even then

- \frac{47}{8} < t - 2 < \frac{47}{8}

a < u < b

then

a < u and u < b

- \frac{47}{8} < t - 2 and t - 2 < \frac{47}{8}

- \frac{47}{8} < t - 2 : t > - \frac{47}{2 2} + 2

t - 2 < \frac{47}{8} : t < \frac{47}{2 2} + 2

Combine the intervals

t > - \frac{47}{2 2} + 2 and t < \frac{47}{2 2} + 2

Merge Overlapping Intervals

- \frac{47}{2 2} + 2 < t < \frac{47}{2 2} + 2

(n \cdot 5) \cdot 4 = (4 \cdot 5) \cdot 2

3 (x + 9)^{2} = 36

4 - x = 3

0 = 3 t^{2} - 3

x^{4} + 3 x^{3} + 6 x^{2} + 12 x + 8

What is -16t^2+64t+80>50 ?
The solution to -16t^2+64t+80>50 is -(sqrt(47))/(2sqrt(2))+2<t<(sqrt(47))/(2sqrt(2))+2