What is 114-36k-6k^2>0 ?

The solution to 114-36k-6k^2>0 is -2sqrt(7)-3<k<2sqrt(7)-3

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114-36k-6k^2>0

114 - 36 k - 6 k^{2} > 0

- 27 - 3 < k < 27 - 3

Interval Notation

(- 27 - 3, 27 - 3)

Decimal Notation

- 8.29150 \dots < k < 2.29150 \dots

Solution steps

114 - 36 k - 6 k^{2} > 0

Rewrite in standard form

- k^{2} - 6 k + 19 > 0

Complete the square

- k^{2} - 6 k + 19 : - (k + 3)^{2} + 28

- (k + 3)^{2} + 28 > 0

Move

28

to the right side

- (k + 3)^{2} > - 28

Multiply both sides by

- 1

(k + 3)^{2} < 28

For

u^{n} < a

, if

n

is even then

- 28 < k + 3 < 28

a < u < b

then

a < u and u < b

- 28 < k + 3 and k + 3 < 28

- 28 < k + 3 : k > - 27 - 3

k + 3 < 28 : k < 27 - 3

Combine the intervals

k > - 27 - 3 and k < 27 - 3

Merge Overlapping Intervals

- 27 - 3 < k < 27 - 3

\frac{4}{5} \cdot (- \frac{1}{4})

\frac{\frac{π}{4}}{π} = 0

lo g_{1.1} (2)

4 (x + 1) - x = 3 (x - 1) + 3

12 5^{\frac{1}{2}}

What is 114-36k-6k^2>0 ?
The solution to 114-36k-6k^2>0 is -2sqrt(7)-3<k<2sqrt(7)-3