What is |x-2|^2-2|x-2|-15>0 ?

The solution to |x-2|^2-2|x-2|-15>0 is x 7

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|x-2|^2-2|x-2|-15>0

∣ x - 2 ∣^{2} - 2 ∣ x - 2 ∣ - 15 > 0

x < - 3 or x > 7

Interval Notation

(- \infty, - 3) \cup (7, \infty)

Solution steps

∣ x - 2 ∣^{2} - 2 ∣ x - 2 ∣ - 15 > 0

Find positive and negative intervals

x < 2, x \geq 2

Solve the inequality for each interval

x < - 3 or x > 7

k^{2} + 17 k + 66

\frac{4}{3} \cdot 4

14 + 17 x - 6 x^{2}

\frac{x ^{5}}{x ^{2}}

(3 - 7 i)^{2}

What is |x-2|^2-2|x-2|-15>0 ?
The solution to |x-2|^2-2|x-2|-15>0 is x<-3\lor x>7