What is x^2+3x-15<0 ?

The solution to x^2+3x-15<0 is (-sqrt(69)-3)/2 <x<(sqrt(69)-3)/2

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x^2+3x-15<0

x^{2} + 3 x - 15 < 0

\frac{- 69 - 3}{2} < x < \frac{69 - 3}{2}

Interval Notation

(\frac{- 69 - 3}{2}, \frac{69 - 3}{2})

Decimal Notation

- 5.65331 \dots < x < 2.65331 \dots

Solution steps

x^{2} + 3 x - 15 < 0

Complete the square

x^{2} + 3 x - 15 : (x + \frac{3}{2})^{2} - \frac{69}{4}

(x + \frac{3}{2})^{2} - \frac{69}{4} < 0

Move

\frac{69}{4}

to the right side

(x + \frac{3}{2})^{2} < \frac{69}{4}

For

u^{n} < a

, if

n

is even then

- \frac{69}{4} < x + \frac{3}{2} < \frac{69}{4}

a < u < b

then

a < u and u < b

- \frac{69}{4} < x + \frac{3}{2} and x + \frac{3}{2} < \frac{69}{4}

- \frac{69}{4} < x + \frac{3}{2} : x > \frac{- 69 - 3}{2}

x + \frac{3}{2} < \frac{69}{4} : x < \frac{69 - 3}{2}

Combine the intervals

x > \frac{- 69 - 3}{2} and x < \frac{69 - 3}{2}

Merge Overlapping Intervals

\frac{- 69 - 3}{2} < x < \frac{69 - 3}{2}

3 x - 12

\frac{3}{49}

\frac{63}{7}

23 y + 50 + 27 y = 50 y + 50

6 x^{2} + 5 x - 21

What is x^2+3x-15<0 ?
The solution to x^2+3x-15<0 is (-sqrt(69)-3)/2 <x<(sqrt(69)-3)/2