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Popular >

5x^2-10x+1>0

Solution

5 x^{2} - 10 x + 1 > 0

Solution

x < - \frac{2}{5} + 1 or x > \frac{2}{5} + 1

+2

Interval Notation

(- \infty, - \frac{2}{5} + 1) \cup (\frac{2}{5} + 1, \infty)

Decimal Notation

x < 0.10557 \dots or x > 1.89442 \dots

Solution steps

5 x^{2} - 10 x + 1 > 0

Complete the square

5 x^{2} - 10 x + 1 : 5 (x - 1)^{2} - 4

5 (x - 1)^{2} - 4 > 0

Move

4

to the right side

5 (x - 1)^{2} > 4

Divide both sides by

5

(x - 1)^{2} > \frac{4}{5}

For

u^{n} > a

, if

n

is even then

x - 1 < - \frac{4}{5} or x - 1 > \frac{4}{5}

x - 1 < - \frac{4}{5} : x < - \frac{2}{5} + 1

x - 1 > \frac{4}{5} : x > \frac{2}{5} + 1

Combine the intervals

x < - \frac{2}{5} + 1 or x > \frac{2}{5} + 1

Popular Examples

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2 7^{\frac{1}{3}} \cdot 2 7^{\frac{4}{3}}

x^{2} + 4 x - 77 = 0

9 x^{2} + 21 x - 8 = 0

5 x - 19 \leq 1

factor u^2-6u-7 factor

u^{2} - 6 u - 7

Frequently Asked Questions (FAQ)

What is 5x^2-10x+1>0 ?
The solution to 5x^2-10x+1>0 is x<-2/(sqrt(5))+1\lor x> 2/(sqrt(5))+1