What is -x^2-7x+10>0 ?

The solution to -x^2-7x+10>0 is (-sqrt(89)-7)/2 <x<(sqrt(89)-7)/2

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-x^2-7x+10>0

- x^{2} - 7 x + 10 > 0

\frac{- 89 - 7}{2} < x < \frac{89 - 7}{2}

Interval Notation

(\frac{- 89 - 7}{2}, \frac{89 - 7}{2})

Decimal Notation

- 8.21699 \dots < x < 1.21699 \dots

Solution steps

- x^{2} - 7 x + 10 > 0

Complete the square

- x^{2} - 7 x + 10 : - (x + \frac{7}{2})^{2} + \frac{89}{4}

- (x + \frac{7}{2})^{2} + \frac{89}{4} > 0

Move

\frac{89}{4}

to the right side

- (x + \frac{7}{2})^{2} > - \frac{89}{4}

Multiply both sides by

- 1

(x + \frac{7}{2})^{2} < \frac{89}{4}

For

u^{n} < a

, if

n

is even then

- \frac{89}{4} < x + \frac{7}{2} < \frac{89}{4}

a < u < b

then

a < u and u < b

- \frac{89}{4} < x + \frac{7}{2} and x + \frac{7}{2} < \frac{89}{4}

- \frac{89}{4} < x + \frac{7}{2} : x > \frac{- 89 - 7}{2}

x + \frac{7}{2} < \frac{89}{4} : x < \frac{89 - 7}{2}

Combine the intervals

x > \frac{- 89 - 7}{2} and x < \frac{89 - 7}{2}

Merge Overlapping Intervals

\frac{- 89 - 7}{2} < x < \frac{89 - 7}{2}

\frac{1}{( x - 2 )} \geq 0

\frac{( x + 1 ) ( x + 3 )}{x ( x - 2 )} < 0

(1) (x - 4) (x + 2) > 0

4 x^{2} - 21 x + 20 > 0

\frac{( x - 2 ) ^{2} ( x + 1 )}{( x - 3 )} > - 0

What is -x^2-7x+10>0 ?
The solution to -x^2-7x+10>0 is (-sqrt(89)-7)/2 <x<(sqrt(89)-7)/2