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Popular >

x^2-2x-1>= 0

Solution

x^{2} - 2 x - 1 \geq 0

Solution

x \leq - 2 + 1 or x \geq 2 + 1

+2

Interval Notation

(- \infty, - 2 + 1] \cup [2 + 1, \infty)

Decimal Notation

x \leq - 0.41421 \dots or x \geq 2.41421 \dots

Solution steps

x^{2} - 2 x - 1 \geq 0

Complete the square

x^{2} - 2 x - 1 : (x - 1)^{2} - 2

(x - 1)^{2} - 2 \geq 0

Move

2

to the right side

(x - 1)^{2} \geq 2

For

u^{n} \geq a

, if

n

is even then

x - 1 \leq - 2 or x - 1 \geq 2

x - 1 \leq - 2 : x \leq - 2 + 1

x - 1 \geq 2 : x \geq 2 + 1

Combine the intervals

x \leq - 2 + 1 or x \geq 2 + 1

Popular Examples

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- 3 y^{2} + 15 y - 18 = 0

8 n^{2} + 13 n = 0

2 x^{2} - 2 x - 7 = 0

Frequently Asked Questions (FAQ)

What is x^2-2x-1>= 0 ?
The solution to x^2-2x-1>= 0 is x<=-sqrt(2)+1\lor x>= sqrt(2)+1