What is |x^2-3x-10|<10 ?

The solution to |x^2-3x-10|<10 is (-sqrt(89)+3)/2 <x<0\lor 3<x<(sqrt(89)+3)/2

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|x^2-3x-10|<10

x^{2} - 3 x - 10 < 10

\frac{- 89 + 3}{2} < x < 0 or 3 < x < \frac{89 + 3}{2}

Interval Notation

(\frac{- 89 + 3}{2}, 0) \cup (3, \frac{89 + 3}{2})

Decimal Notation

- 3.21699 \dots < x < 0 or 3 < x < 6.21699 \dots

Solution steps

x^{2} - 3 x - 10 < 10

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- 10 < x^{2} - 3 x - 10 < 10

x^{2} - 3 x - 10 > - 10 and x^{2} - 3 x - 10 < 10

(x < 0 or x > 3) and \frac{- 89 + 3}{2} < x < \frac{89 + 3}{2}

Merge Overlapping Intervals

\frac{- 89 + 3}{2} < x < 0 or 3 < x < \frac{89 + 3}{2}

\frac{1}{2 ^{4}}

\frac{2}{3} \cdot \frac{3}{2}

3 x^{2} - 7 x - 10

25 r^{2} + 80 r + 64 = 0

- x^{2} + 3 x - 2 = 0

What is |x^2-3x-10|<10 ?
The solution to |x^2-3x-10|<10 is (-sqrt(89)+3)/2 <x<0\lor 3<x<(sqrt(89)+3)/2