What is x^2+5x-16<0 ?

The solution to x^2+5x-16<0 is (-sqrt(89)-5)/2 <x<(sqrt(89)-5)/2

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x^2+5x-16<0

x^{2} + 5 x - 16 < 0

\frac{- 89 - 5}{2} < x < \frac{89 - 5}{2}

Interval Notation

(\frac{- 89 - 5}{2}, \frac{89 - 5}{2})

Decimal Notation

- 7.21699 \dots < x < 2.21699 \dots

Solution steps

x^{2} + 5 x - 16 < 0

Complete the square

x^{2} + 5 x - 16 : (x + \frac{5}{2})^{2} - \frac{89}{4}

(x + \frac{5}{2})^{2} - \frac{89}{4} < 0

Move

\frac{89}{4}

to the right side

(x + \frac{5}{2})^{2} < \frac{89}{4}

For

u^{n} < a

, if

n

is even then

- \frac{89}{4} < x + \frac{5}{2} < \frac{89}{4}

a < u < b

then

a < u and u < b

- \frac{89}{4} < x + \frac{5}{2} and x + \frac{5}{2} < \frac{89}{4}

- \frac{89}{4} < x + \frac{5}{2} : x > \frac{- 89 - 5}{2}

x + \frac{5}{2} < \frac{89}{4} : x < \frac{89 - 5}{2}

Combine the intervals

x > \frac{- 89 - 5}{2} and x < \frac{89 - 5}{2}

Merge Overlapping Intervals

\frac{- 89 - 5}{2} < x < \frac{89 - 5}{2}

x^{3} + 7 x^{2} + 10 x

\frac{4 - x}{x + 1} > - 3

\frac{7}{9} - \frac{1}{6}

x + 14 = - 8

x^{2} - 6 x = 91

What is x^2+5x-16<0 ?
The solution to x^2+5x-16<0 is (-sqrt(89)-5)/2 <x<(sqrt(89)-5)/2