What is |x^2-x|-5<3 ?

The solution to |x^2-x|-5<3 is (-sqrt(33)+1)/2 <x<(sqrt(33)+1)/2

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|x^2-x|-5<3

x^{2} - x - 5 < 3

\frac{- 33 + 1}{2} < x < \frac{33 + 1}{2}

Interval Notation

(\frac{- 33 + 1}{2}, \frac{33 + 1}{2})

Decimal Notation

- 2.37228 \dots < x < 3.37228 \dots

Solution steps

x^{2} - x - 5 < 3

Move

5

to the right side

x^{2} - x < 8

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- 8 < x^{2} - x < 8

x^{2} - x > - 8 and x^{2} - x < 8

True for all x and \frac{- 33 + 1}{2} < x < \frac{33 + 1}{2}

Merge Overlapping Intervals

\frac{- 33 + 1}{2} < x < \frac{33 + 1}{2}

n^{2} + 77 = 0

5 x + 4 = 3 x - 4

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

14 a^{2} - 15 a + 4

0 = 3 x^{2} - 12

What is |x^2-x|-5<3 ?
The solution to |x^2-x|-5<3 is (-sqrt(33)+1)/2 <x<(sqrt(33)+1)/2