What is -x^2+81x-81>0 ?

The solution to -x^2+81x-81>0 is (-9sqrt(77)+81)/2 <x<(9sqrt(77)+81)/2

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Popular >

-x^2+81x-81>0

- x^{2} + 81 x - 81 > 0

\frac{- 9 77 + 81}{2} < x < \frac{9 77 + 81}{2}

Interval Notation

(\frac{- 9 77 + 81}{2}, \frac{9 77 + 81}{2})

Decimal Notation

1.01266 \dots < x < 79.98733 \dots

Solution steps

- x^{2} + 81 x - 81 > 0

Complete the square

- x^{2} + 81 x - 81 : - (x - \frac{81}{2})^{2} + \frac{6237}{4}

- (x - \frac{81}{2})^{2} + \frac{6237}{4} > 0

Move

\frac{6237}{4}

to the right side

- (x - \frac{81}{2})^{2} > - \frac{6237}{4}

Multiply both sides by

- 1

(x - \frac{81}{2})^{2} < \frac{6237}{4}

For

u^{n} < a

, if

n

is even then

- \frac{6237}{4} < x - \frac{81}{2} < \frac{6237}{4}

a < u < b

then

a < u and u < b

- \frac{6237}{4} < x - \frac{81}{2} and x - \frac{81}{2} < \frac{6237}{4}

- \frac{6237}{4} < x - \frac{81}{2} : x > \frac{- 9 77 + 81}{2}

x - \frac{81}{2} < \frac{6237}{4} : x < \frac{9 77 + 81}{2}

Combine the intervals

x > \frac{- 9 77 + 81}{2} and x < \frac{9 77 + 81}{2}

Merge Overlapping Intervals

\frac{- 9 77 + 81}{2} < x < \frac{9 77 + 81}{2}

(2 - 2 i)^{2}

\frac{15 a ^{3}}{3 a}

x + 6 = 7

- 0.1 x^{2} + 90 x - 20250 = 0

30 - 8 x < 6

What is -x^2+81x-81>0 ?
The solution to -x^2+81x-81>0 is (-9sqrt(77)+81)/2 <x<(9sqrt(77)+81)/2